text:
Is it important for postdocs to have a "postdoc mentor"?
I'm in pure math. It seems like "postdoc mentors" are common nowadays in U.S. universities. The idea is that you do a postdoc under the supervision of someone whom you can write papers with. My impression though is that a lot of mathematicians didn't have postdoc mentors. Would it be a bad sign to not have a postdoc mentor? Would it be negative for productivity and developing a publication record and recommendation letters?

Note that in many cases funding agencies are now attaching mentoring requirements to the grants that pay for postdocs.  For example, the NSF requires that proposals include a "Postdoctoral Researcher Mentoring Plan."

It is true that, long ago, when "post docs" were not as numerous as now, there was no idea at all that you'd have a mentor. Rather, even though you'd be a new PhD, you were "an expert". And, also, long ago, joint papers were not so common.
That culture has not disappeared, unfortunately. Yes, in my opinion, sensible people of_course think in terms of mentoring... But this viewpoint is not universal.
Joint papers are a yet-subtler thing: good to have a collaboration, but these days, still, a joint paper with a senior person (in math) may be less of a CV-boost than a solo paper. As an "old person" myself, I try to give useful advice to junior people without trying to get my name on their papers.
EDIT: to answer more of the question, ... letters of recommendation for your next job do need to come from people who have engaged with you. This doesn't have to be a "mentor", though obviously a person who takes that role should be in a good position to write a helpful letter. At least in the old days ^tm, a postdoc's goal was to make a good impression on at least a few senior people in the dept, for letters. Seminar talks were the usual way.
I think the letter-of-recommendation concern is more substantial than "productivity", in saner parts of math. :)

Does it make sense to have a postdoc mentor who is unfamiliar with your work and doesn't work closely in your area/ with whom there is little chance of collaboration?

@Mehta I'm not an academic, but I've found reasonable value in mentors who are decidedly not people who I'd go to for "technical" problems. The separation helps them focus on advising you in career/interpersonal/long-term questions that I think become muddy for people who are "too close" to your situation.

I think there is some confusion about what a "postdoc mentor" is actually supposed to do.
But, to start with, let me just say that I don't think anyone can be successful in an academic career without a mentor. A mentor is supposed to help a mentee go through their career by providing advice on the many things a newly graduated PhD simply cannot know: How to deal with reviewing papers, how applications are read by hiring committees, how to become a mentor to students themselves, how to deal with authorship disputes, how to write grant applications, and many other things. That is what a mentor is supposed to do, and because so many things in academia are sub-discipline-specific, it only makes sense that such a mentor comes from the same sub-discipline.
That often leads to joint papers, but that is a side effect and not the main reason to have a mentor for postdocs. The main reason is simply to ensure that the people we hire into postdoc positions don't fall through the cracks but are successful in their careers!

That's in such contrast with the advice I had been given: don't worry about postdoc mentors. Just focus on publishing.

Did Einstein have a mentor in the Swiss patent office? It's incredibly useful to have a mentor, but not everybody actually needs one. You should have a mentor, and you should go to them if you have problems with or questions about anything, but many postdocs don't interact with theirs that much (some do!).

"how to write grant applications" <-- this is probably the biggest help, along with advice around looking at applying for a more permanent position.

@PeterShor I don't actually know whether Einstein had a mentor, but (i) I think it's not useful to compare anyone to Einstein, nor (ii) is an example from 115 years ago useful for today.

This depends on the individual and the department that you join, in math, anyway. If there are a few (or a lot) faculty in your specialty and they hold periodic seminars to discuss one another's work, then a mentor probably isn't needed.
But if you still feel a bit shaky in your research ability, then a mentor might help give you a boost. I don't think it would be a bad sign to not have a mentor (or to have one), but you want to make enough faculty contacts and earn the respect of your colleagues so that you get a boost for your next steps.
Of course, there are a lot more joint papers these days than there were in the past. You want the opportunity for collaboration, however you can arrange it.


text:
PhD Mathematics Admission Advice
Some background on me:
I graduated in 2020 with my BS in Accounting with a minor in Mathematical Sciences from a non-special public university. I decided I wanted to make an educational career change with only 1.5 years of undergrad schooling left. Mathematics courses I took in that time were calc 2, calc 3 (taught myself calc 1), differential equations, linear algebra, and real analysis. I got A's in all of them. I was lucky enough to be admitted into an MS in applied math program in my state at a relatively well known private school in the tristate area knowing I didn't have a serious shot at being admitted to a PhD program. This first semester I am taking topology, numerical linear algebra for big data, and probability theory. I am concentrating in data science but still taking more pure mathematics courses as electives.
I plan on sending out PhD applications for the Fall 2022 cycle during the fall semester of 2021. At that time I would be enrolled in foundations of algebra 1 (which is just abstract algebra), functional analysis 1, and numerical analysis. I am hoping to do a research project with a professor this upcoming summer. With that said, I know some of the very important things for the application are the letter writers (of which 1 professor at my school is pretty well known). Other than that, I plan on retaking the standard GRE which i did not do well on the first time, and potentially taking the subject GRE. What would this community say my chances are at being admitted to a top 50 university with funding? I know it's kind of a hard question to answer but if theres any other info I can provide please tell me. I would also accept any advice you could give me. I will most likely just be looking to apply to pure math phd programs while planning to do my research in a more applied area.
Thanks.

I added the United States country tag, but feel free to change it if it's wrong.

Your plans seem a bit odd -- you are concentrating in data science, and plan to do research in an applied area, but you hope to apply to programs in pure math? Graduate admissions are difficult to predict, and circumstances can vary widely -- but my first impression is that you might want to either start preparing for your stated goals, or alternatively look for possibilities that your current work might open up. Best of luck to you.

Although some people might reasonably think that "pure math" courses are irrelevant to your larger goals, I would claim that the popular distinction between "pure" and "applied" math is both scientifically meaningless, and potentially hazardous to people trying to get started.
Having fluency with basic ideas of abstract mathematics ("algebra", "topology", and such) is inestimably useful. Illiteracy in these things makes it impossible to really know what the substance of many "applied" conversations may be.
The ideas in "pure/abstract" math are not at all disjoint from "the real world". They were all motivated by the desire to understand things. Yes, some self-styled "applied math" people pretend that all they need is computer time, and some self-styled "pure math" people pretend that whatever they do is disconnected from reality, and is practically useless. This is all silly, in my opinion.
In particular, having a basic grounding in "abstract" math will make you a far better candidate for any reasonable math program, whether eventually aiming at something "applied" or "not".

If you mean a TA by "funding" then you would probably be fine. But it is impossible to say until you apply. Make sure you have good letters of recommendation.
But "free ride" funding is not so obvious. A TA normally comes with free tuition as well as a living stipend.
And note that the GRE is being de-emphasized now in many places. But it is the application that gives you real information. Apply to a variety of places to give yourself more options.

source: Stack Exchange

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

sort: votes


text:
Is a PhD in a small university in a small country restrictive for an academic career abroad?
I am located in a small European country and studying computer science in one of its Universities, admittedly not the most prestigious one. I am set to finish my undergraduate degree at most a year from now. Recently, an opportunity has come up as I have been offered a PhD position right after I am done with my bachelor's. Along with that, I have been offered a position in a EU funded project that is right on my field of interest.
I am struggling to make the choice as I would have to give an answer before I am done with my degree so that if I decline they will have the time to look for someone else to take the spot.
My purpose and hope is to have an academic career in a university that does significant research in the field I am passionate about. However, those universities even in Europe seem to be the most prestigious ones (Oxford, Edinburgh, ETH Zurich etc). I can currently boast a few conference publications, some upcoming journal publications, and hopefully two more will come out of my undergraduate thesis currently underway. All in all I hope to have at least 8 papers to my name by the time I get my bachelor's. I should specify all my works but one are research focused, not surveys.
My dilemma is as follows:
Do I choose to do my PhD in my university and hope to break in the academic world abroad with my post doc?
Do I do a master's elsewhere and then hope to get funding for my PhD abroad?
Or can I hope that I will get accepted for a PhD position abroad if I apply after my undergraduate is done? This would be the optimal scenario but I have not come to contact with any cases that did their PhD right after their undergrad, much less in a different institution. I guess I am wondering what my chances of pulling this through would be, and if they are low to zero, which of the aforementioned two scenarios would help me more to pursue an academic career in the Computer Science field?
Thanks for any insight and advice.

Where do the good students with PhDs at the school you’re considering get jobs in practice?

If your publications are in respectable, refereed CS conferences then you would be an extremely competitive candidate for top-20 computer science programs. Many PhD graduates don't have eight publications to their name after five years of intensive research.
If you are talking about local conferences, student events, or unrefereed/lightly refereed workshops then of course this is much less impressive, but still - it clearly shows you are interested in research and positions you very well when applying.
More importantly perhaps, by working so much on research with someone, you get the opportunity to have an enthusiastic letter writer who will vouch for your qualities (as opposed to a letter writer who'll say that you just took their class or something of that sort).
There are two major things to consider when applying for a PhD program: the fit of a potential advisor, and the quality of the program. Both will dramatically affect your academic success and career trajectory.
I have personally seen candidates who got offered a faculty position over a stronger candidate who graduated from a less prestigious school. It's a bad and elitist practice, but departments sometimes want to position themselves as stronger by hiring Ivy League (or equivalent) graduates.
On the other hand, if you absolutely love what you do and work well with an advisor right now who's offering you a position, that might be a very good reason to stay on, even if the university is not as prestigious.
However, in any case, apply broadly, and don't be afraid of applying to top programs. Do your due diligence - research the programs that you might like, and potential advisors in every school that you apply to. Check how well their students did, whether they're research active, and whether they're working on stuff that you care about.
The fact that you're just an undergraduate is not an issue: many CS grad programs offer a MSc.+PhD/direct to PhD options (I did my PhD straight from undergraduate), and if your research credentials are as stellar as you describe, then good universities will fight hard to get you admitted.
If you get admitted to a top school (Oxford, EPFL, Harvard, MIT etc.) - awesome! If not - you can always fall back to your current institution's graduate program. Even if you land an offer that you're not super happy about (say, no obvious advisor fit), you can try and use it to ask your current institution for perks (e.g. a scholarship or a stipend).
Good luck!

This is important career advice and should be given by someone who you trust who knows you personally.  If no one comes to mind, ask your existing professors in the field.
As you suspect, there are powerful reputational and network effects from prestigious programs.  It would be hard to argue that your employment prospects after graduating Cambridge are fairly good! You have heard of it and respect it. Your question is - how does your future employer feel about your Uni?  Have they heard of it? Do they respect it? Do they teach what you want to learn?
The question is very specific to your field.  Perhaps your Uni is universally known for the subject, or has undeniable geographic advantages - like studing Marine Biology at U-Hawaii or being across the street from CERN. It is hard to tell how strong that reach is until you have dipped your toes in the job market.
Note: while you can trust your teachers to guide you honestly, do not expect them to talk poorly of their current institution to a student. They will not.  Simply be aware that if the local institution "is good enough" is not the same as saying "we are one of the top institutions in the world, of course you should stay."

I have been thinking more about this. 8 publications is an awful lot. Nearly all undergraduates have 0. You absolutely should be given a serious look by nearly any institution. Expect to get some responses if you put in more than a handful of appications. If you put in many applications and hear nothing, something strange is happening and you need an outside consultation.

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


text:
Postdoc in the US : what salary should I ask for
I live in France and I'm currently applying for postdoc positions in fundamental mathematics, at several universities in the US and elsewhere. For my application at the University of Denver, I'm asked to give my desired salary, and I have no idea what to answer... I don't know at all what are the standards in the US, I don't even know if it's homogeneous or depends on states... So two questions:
1) Do you have an idea of what could be a standard income for such a position? (To be more precise, it's a visiting assistant professorship with a teaching load of five undergraduate courses over three quarters during the 9-month academic year.)
2) I don't know if the desired salary is taken into account during the search process. Do you think I should ask for a lower salary in order to have more chances to be hired? Or should I, on the contrary, ask for a higher one and expect they will bargain?
Thank you in advance, I'm a bit lost since it doesn't work at all in the same way in France...

Likely the post doc position has a well defined salary. However, the application process asks for a salary for all positions. You could ask the professor the position is with.

That's a weird thing for them to ask at the application stage. One suggestion for where to look for information: Public Universities in the US are required to publish the salaries of their employees. University of Denver is not public, but you can look up the salary of a comparable position at a nearby public university.

I'll note that the cost of living in the US varies greatly from place to place.

I would not describe the position as a 'standard' postdoc: a teaching load of 5 courses over 9 months would leave you little time for research. At least in CS, postdoc positions involve little to no teaching. In that spirit, I would not compare your salary to that of a postdoc (those would be something like 60-70k per annum in CS, with some variation), but perhaps to that of an adjunct lecturer

Looking at the ad, it’s clear that they’re having you apply through a web page that is used for all of their staff positions.  For a VAP position  like this, most applicants won’t currently be in a position with a salary that UD must beat.  For more senior staff positions it makes more sense to ask this question.

VAP (mostly teaching) is very different from a postdoc (mostly research).

First, it is important to understand that a visiting assistant professor position isn’t a postdoc in the sense that you are being hired primarily for research and based on your research background.  This position will be funded by the institution rather than by grants. Teaching will be an important part of the job, and your teaching experience will be important in the selection process.
The American Mathematical Society publishes an annual survey of faculty salaries.  I’d encourage you to look at the survey to get a sense of the range of faculty salaries in the US. Figure that a VAP will be paid slightly less than a first year tenure track assistant professor.  If I had to guess, I’d expect a position like this at UD to pay somewhere between $60K and $70K.

To give you a reference point: A postdoc salary is around 50.000 USD in your field, before tax. As you will be working on a J1 visa, your salary is exempt from certain significant taxes (social security and medicare) during the first two years.

According to the Wiki page you linked, However, they are subjected to other applicable federal, state, and local taxes.

yes, but j1 is exempt from 1 of them and the other is very low in amount

According to this calculator, if you are a single person earning 50,000 a year, you pay $9,075 federal tax. which is not low in amount (18%).

This is not so strange.  They want to get you at a cheaper price.  NEVER quote a salary first for any job.  Always let them make the offer.  Just write in "TBD" or negotiable or leave it blank.  In discussions, just say that it depends.  If they really push you hard, just ask them to make a written offer and you will respond then.
Usually it is not a big drama and you can just brush it off.  Don't put a number down...

I also recommend highly to do some research and find out what the going rate is for postdoc fellowships in your field in the US (and for your level of competitiveness).  You still won't want to write down a number.  But you need to know that when evaluating offers.  As with any job there can be other factors like benefits, cost of living, duties, fun place to live, advancement.  [All that said, the job with the higher $$ is almost always the best fit...they are showing how much they care with that.  And it can affect future salary offers as well.  Never go in low.]

I'm not sure this answers the question. OP is clearly trying to do some research (hence their post here), and they are in fact required to write down a number.


text:
Would I have to conduct an experiment to write a scientific paper?
I recently got a book named How to write and publish a Scientific Paper by Robert A. Day and Barbara Gastel. The book doesn't really explain the "background" of a scientific paper.  Would I have to conduct my own, original experiment in order to write a scientific paper, or could I just use the data from other experiments to make an orignal claim?

Possible duplicate of https://academia.stackexchange.com/questions/122360/would-i-need-to-conduct-some-sort-of-experiment-before-writing-a-scientific-pa

A paper should contain something original. It doesn’t need to be an original experiment. It could be a new theory that explains data collected by others. I suggest you try to find similar papers and read them to see what they have done.

There are many non-experimental sciences: mathematics, history, sociology, you name it.

It might be useful to look at some of the manuscripts deposited in arXiv, especially those in areas you are most familiar with. Also, many journals have their published papers freely available (sometimes after a handful of years).

One other thing to consider -- what do you mean by "experiment"? In computer science or high-energy physics theory, for example, there are "numerical experiments" (results of computer code) that are very much publishable/useful, but not an "experiment" in the traditional sense.

A scientific paper doesn't necessarily have to be based on an original experiment. You can write a paper that's a review (whether systematic or just comprehensive literature review) of the current body of literature for a specific topic or a meta analysis. You can also write papers that are derived from original experiments that you ran or secondary analyses of data from experiments run by others.
It depends on what the purpose of the paper is. If it's to introduce an entirely new phenomenon or theory, original experiments are pretty common. If it's to argue that current theories or concepts may be flawed in certain ways or you want to add something to existing literature, then meta analyses, original experiments, and secondary data analyses can all be relatively common and appropriate. If it's to introduce a new perspective to a theory or concept, then comprehensive literature reviews may suffice. This can also depend on what field you're in, so consider what the norms are in your field and whether the journal you want to publish in accepts the specific paper type.


text:
Is it ever appropriate to ask a professor to be a business advisor?
Myself and a few business partners of mine are working to develop a software product, in which I am responsible for building and all other technical aspects. At the same time, I'm currently pursuing a secondary degree in Computer Science at a local university. As my responsibilities within our business include securing a competent technical advisor, a suggestion was raised by my colleagues to inquire with my professors as to if they'd be willing to take on a limited advisory role in exchange for some amount of company ownership.
Is this at all common in the academic world? There are past professors in which I've excelled in their classes, had positive relationships and would consider their knowledge in such a role incredibly valuable. Additionally, I also know a few of them are not full-time with the university, but serve as guest lectures with ongoing careers in the software field.
I've been told this isn't an entirely uncommon practice, but I can also foresee a number of ethical issues and conflict of interest surrounding this idea, given that I'm a student within the program.

Is this at all common in the academic world?

This is quite common in some departments.

I've been told this isn't an entirely uncommon practice, but I can
  also foresee a number of ethical issues and conflict of interest
  surrounding this idea, given that I'm a student within the program.

There are indeed substantial conflict of interest problems with this, though they are somewhat less if the professor is not your direct supervisor. Regardless, there are almost certainly systems in place at your university to handle these in some way.
In short: It's certainly possible, not particularly exotic, but will require some extra effort.

What's the specific relationship between you and your professor? If the professor is currently teaching a class you are taking, advising your thesis, etc. then it may be considered a conflict of interest.
However, if you had a student-professor relationship but are no longer in said relationship, and don't foresee any future ones, then I personally don't see any ethical issues. If you are merely a student of the program but the professor of interest has no direct advisory or administrative role that's instrumental to your academic success, then there essentially is no conflict of interest from what I can see.
If the professor does has some key role, then it may be advisable to wait until you graduate or it's 100% clear that you have no extraneous relationship with the professor that would result in conflict of interest.
I don't think it's a common thing in the academic world, but that might just be because a lot of professors don't have work experience outside academia and never thought about venturing into the unknown. This could also depend on the department (e.g., a lot of Business Professors seem to do consulting work on the side).

Due to the mentioned ethical aspects you should avoid any financial relationship with professors of which you are still taking courses.
On the other hand, it is happening quite often that a professor is supporting a start up and compensation can be either money, company ownership, or sometimes just personal satisfaction.

It's common in business schools.  I just would be a little wary of what is involved for each party.  Maybe you get a few ideas/coaching and the name to flaunt around (and they do to).  But you are going to have to drive the business.


text:
Do I have to disclose the exchange program of participating student as funding in a paper?
I am currently writing a paper together with an exchange student of an international academic internship program. As it is common practice, I disclose the research grant, which funds my work. However, the student is paid by the exchange program. He did most of the work and is first author. I am his supervisor and continuously guided his work, though.
Would it be required or is it good practice to disclose the source of his payment or is the grant of my superordinated research project sufficient?

Why not? It costs nothing to add. Withholding acknowledgements has no advantages.

It's good manners to acknowledge all sources of funding, and in some cases, may actually be mandated by the funding body. It also costs nothing to add a sentence in the acknowledgements, so overall you should certainly acknowledge the student's funding.

It sounds like you've benefitted from this internship program (it brought you a student who does successful work who you didn't have to pay!).
Not only should you acknowledge this funding as good manners and perhaps a required policy, you should be eager to do so as a way to credit the program for this benefit!


text:
In the USA, do college courses deeply differ from high school courses?
I'm interested in school systems, and I have a question regarding the "college" level. (I have a French background).
When I look at college math or physics books, it seems to me that there is no big difference with what is taught at the high school level.
By comparison, in France, first year university math or physics books dramatically differ from high school books.
To put my question in a provocative way: what is the purpose of teaching at the college level what students already know from their high school courses? Or don't they? Or, is my vision of college contrary to actual facts?

The aim of educational systems can be quite different, hence the underlying expectations likewise will be different. I think about France where there's a sort of culling process. The American system attempts to accommodate and retain. As a result it seems in the latter the lines between early undergraduate and high school continues to blur, a general lowering of standards in one, not a raising in the other.

Your Question would be improved if you explained the details of how your "first year university math or physics books dramatically differ from high school books" in France.

"The American system attempts to accommodate and retain." Or, "no child left behind" becomes "no child allowed to get in front".

@Dirk: India has 23 official languages. Per the 2011 census, there were 259,678 people who spoke English as their first language, 83,125,221 second- and 45,993,066 third language speakers. Indians who post at StackExchange are a highly educated and nonrepresentative minority.

@Aruralreader, "not a raising in the other" would need citation.

@Mayou36 - or, instead of a citation, you could just live in the USA for the last 30 years and look around you.

@davidbak It's kinda a mixed bag. Some high schools graduate students with a full associate's degree (and actually involve real college coursework), AP courses offer some college level material. Though to be fair taking part in these courses isn't required, and if a student followed the "stock" curriculum they'd graduate after learning precalc. For me personally in the US I would have very much liked to take more difficult coursework (and I actually could've), but nobody brought it up and I assumed it wasn't possible to do so. I just didn't know what options were out there.

@jrh - those schools - and their students - are definitely the minority though.  The vast majority ... especially out of public schools ....

The content of textbooks is definitely not the only aspect of a course that can be varied. In my North American experience, expectations for college students is far higher than expectations for high school students (even when on nearly identical material), and individual benefit-of-doubt much lower.

@davidbak, my comment was the other way around. It was my understanding from the comments (alephzero) that all get the same basically. What was claimed that the alternative would lower the level of the lowest and not raising the highest (so the non-US system). Your comment seems to contradict now alephzeros, is the "no child left behind" a thing? I got confused about what is up now.

First of all, the US has no university system.  It has somewhere around 1500 community colleges offering 2 year degrees and 3500 colleges and universities offering 4-year degrees, all of which run with more independence than an ordinary French university.  (Keep in mind the federal government has established only a tiny handful of universities; public universities are nearly all set up by the individual states.)
Second, you should understand that there is no high-school leaving exam like the bac.  Basically anyone who is willing to sit in the classroom and do a minimal amount of work can get a high school diploma.  Harvard is incredibly selective and it's about as hard to be admitted to Harvard as it is to be admitted to the ENS.  The top 100 or 200 of US universities are all selective, and the average student would not be admitted.  However, most universities and all community colleges will allow anyone with a high school diploma to attend.  (My university officially has admission requirements based on high school grades, but high school grades have been inflated to such an extent that these requirements are almost meaningless, and the admissions office routinely gives waivers to these requirements anyway.)  About 85% of Americans earn a high school diploma and can attend community college.  (Another several percent obtain a GED.)  Only about 45% of French take and pass the baccalaureate general and can attend university.
At a community college, you should expect that many students do not actually know what you might think they should have learned from high school, and a significant number of students will have trouble with upper elementary material such as adding fractions.  There will even be a few students who are functionally illiterate.

Note: GED = General Education Diploma (informally), a HS equivalent diploma earned by exams and mainly by adults who dropped out of school early.  https://ged.com

For the foreign reader, public universities aren't all of our universities. Idk what % but universities are either state-run or private not federal. Most universities you've probably heard of are private (Stanford, Harvard, Princeton, NYU)

While the public Universities are run by the individual States, they all receive significant federal funds, which gives the federal government a significant say in how they are run.

Comments are not for extended discussion; this conversation has been moved to chat.

This is a US centric answer. Over the past 50 years there has been a vast change in what happens in HS. For example, when I was in school it was extremely uncommon for a HS student to take beginning Calculus. Now the better students do that pretty regularly through the Advanced Placement program which is an attempt to teach college courses in HS.
So, the course in Calc I and Calc II might look the same in an advanced placement course and in a first year college course, but those students who have done well in the advanced placement program (courses and exams) don't have to repeat those courses in college (ideally, anyway). They are able to start at a higher level and it then becomes easier for them to take higher level courses throughout.
But a student who hasn't done "AP" but wants to study math will start with those courses in college.
There are also a few exceptional secondary (HS) schools that teach quite advanced courses, such as multivariate calculus, advanced analysis, and a few others. But they are both difficult to get in to and hard to succeed in (as in lots and lots of work).
At the other end of the scale there are also secondary schools with insufficient trained staff to offer much in the way of math beyond Trigonometry and Analytic Geometry. But, 50 or so years ago, that was the standard for most US schools.
I'm quite certain, however that this model isn't practiced in very much of the rest of the English speaking world. It is quite different in UK, but so is the university system quite different there than here.

The fundamental difference is that the UK has a national curriculum for school education, and two levels of nationally standardized exams usually taken at the minimum school-leaving age (16) and two years later. Students aspiring to go to university would typically take 9 or 10 subjects in the first level exams, and 3 in the second level. University admission to study any subject requires a high enough grade in core subjects (e.g. English and math) at the first level, plus high enough grades in the second exams in the subjects relevant to the university course.

... and the "9 or 10 subjects" examined at a national standard level means there are no mandatory "general education" component in university degree courses.

@alephzero The SAT, ACT, and SAT subject tests act as a de-facto nationwide entrance exam in the US. Opposite would be Japan which, despite recent attempts at standardization, still largely requires institution-specific exams, particularly at prestigious institutions. Also relevant is that the UK (and UK-derived systems) shift one year of college to high school, compared to the US.

@user71659: Community colleges do not have an SAT/ACT requirement, and most 4 year universities have one on paper but will basically admit anyone.  Only a small minority of universities in the US are selective.  Most are de facto open admissions.

While a senior in high school I took college level courses through the high school and received college credit.

This seems like a much more flexible system than the leaving certificate exams.

@AlexanderWoo Same thing in the UK, you have the further education system vs higher. The US community college is referred to as a regional or city college there.

The other answers here are correct. Colleges and high schools across the US are so different (in my opinion the single biggest problem with US education) that it's almost meaningless to speak of how the average high school education compares to the average college education.
However, there is one difference between high school and college in the US that is more or less universal: instructional style. At the high school level, teachers are punished if students don't score sufficiently well on standardized yearly exams. This means that at most high schools, teachers employ a variety of strategies to make sure that as many students perform well on these exams as possible. The philosophy of high school level instruction is "if the students didn't learn it, the teacher failed (and should be punished)." By contrast, the philosophy of college level instruction is usually "if the students didn't learn it, the students failed (and should be punished, e.g. by failing the course)."
Because of this, in high school classrooms, instruction is typically varied and focused on remediation. The onus is on teachers to make sure that students learn. In college classrooms, instruction is typically synonymous with lecture. The onus is on students to learn what the course requires (indeed, even if the professor doesn't teach it).

Difference are good, because parents and students have different desires, needs and wants. I consider this aspect beautiful that a central authority does not have the power to force everyone to be molded to the whim of a central bureaucrat.

@paulj The problem is that the tests are centralized and designed according to the whims of bureaucrats. What's odd is that when students fail to perform on these tests, the teachers usually shoulder the blame, not the bureaucrats who designed the tests.

You already have very detailed answers on the U.S. system. Let me talk a little bit about how a French perspective creates distorted expectations.
In the French system, the curriculum is (essentially) set at the highest level by the Ministry of Education. Much of the nonsense passed as education in some countries (sometimes with sectarian affiliations) is simply illegal in France. The educational content you get in France is tightly controlled. In many other countries (including the U.S.), not so much. There are pros and cons.
Pro: at the time of writing, the French have competent or semi-competent government officials with a tolerance for logic and common sense. Meanwhile in some U.S. schools, Huckleberry Finn and To Kill a Mockingbird are banned.
Con: There are occasional missteps and missteps have huge consequences in France since they affect every student. An example is intolerance for the headscarf: a wonderful, avant-garde idea when it was implemented and almost certainly a huge national embarrassment a few years from now. I can already hear American T.V. networks making fun of the French.
Pro: new knowledge can be disseminated to every student in every part of the country. You don't have regional inequalities like you do in the U.S.. Sure Paris schools have better students on average, but a good student in a small French village will learn: in the U.S., redneck begets redneck.
Con: It takes forever for innovations to find their way into the curriculum as the ageing technocrats retire and are replaced by younger ones with a better grasp of the world around them. In the U.S. a school will not hesitate to teach the earth is a cuboid and if it is, they're ahead of their time, while the French will always lag behind.
Pro: Since bureaucrats at the Ministry of Education, not students nor their parents, set the curriculum, they can choose to emphasize math and technology, while de-emphasizing art and ancient Greek if they feel that's what will take the country forward. Meanwhile in the U.S., students and parents decide what the schools will teach them (schools adapt their curriculum to demand) and if that means teaching that the earth is flat and that the election was stolen, they will.
Con: In France centralization has created a system where it's nearly impossible to switch fields: If you took the literary stream (whatever it's called these days, they rename it every decade), you are unlikely to be able to study math and physics at "university" (I say university, but I include the classes prépas and grandes écoles of course). If you choose the wrong stream at the age of 12, you will pay for the rest of your life. Meanwhile in the U.S. you can major in "Poetry and Chemistry" or "Logic and Religion".
Edit (clarification): There is a great deal more diversity in the United States and other countries than there is in France. It's not just because of population size: Switzerland is also far more diverse than France. French centralization goes back a long way to the days when students who spoke their local dialects were severely punished (Louis the 14th and all that; see how widespread local dialects are today in, say, Spain and Italy compared to France). In France, if you took the "literary" stream, you're not very likely to attempt to take math/science/technology classes. Moreover math is (currently) unusually strong in France, by world standards, as a result of the early specialization. The U.S. system is far more flexible, mainly because it caters to student demands. So yes, many U.S. universities and colleges offer easy subjects, but if the students are willing to pay for it they must be getting something out of it.
That was too long for a comment.

Fun reading, if a tiny little bit polemical. Have my +1 to counterbalance all the downvotes you are sure to get.

Thanks Stephan! I didn't have votes in mind when I wrote ;-)

The US does have accreditation enforcing standards and requiring things that may be out-of-date, essentially acting as your French bureaucrats

@OwenReynolds, but the point is that California and Alabama will have very different standards, and within California different schools will have very different standards. And that's what I'm trying to emphasize in my discussion of the French centralized system. In France when we ban something, we ban it in every French school, including religious schools. And if it's legal and a school attempts to ban it, anyone can take the matter to an ombudsman and the school will be forced to comply.

@PatrickT "Redneck begets redneck?" Isn't it bigger than that, the poverty cycle and ed opps in the US?  Parents beget children.  Social stratification affects everyone.  The "something" they get for their money is debt but for more job opps, not necessarily more education than a HS diploma. Mileage varies.

I guess I'm not sure if you're talking HS or college. Sure, American high schools are locally controlled. Maybe the obvious examples are sex-ed classes not being so much in the bible belt. But American colleges can't quite be so diverse -- every Geology major is looked at every 5(?) years by the same national geology accreditors.

@livresque. Sure, the sources of inequality and social stratification are complex, but educational institutions are typically expected to be a mitigating factor. This is no longer the case in the U.S.: education has become a "buyer's market". The probability of earning more than your parents is approximately 50% down from 90%. See, e.g. https://voxeu.org/article/trends-us-absolute-income-mobility-1940 .

@OwenReynolds, of course I don't mean to say that the Wild West is still with us, but if you look here at how the accreditation system is organized: https://www.accreditedschoolsonline.org/resources/how-college-accreditation-works/ you see a degree of geography-based diversity that simply does not exist in France: France doesn't have an accreditation agency for the North and one for the South. They have the same standards for La Réunion, Tahiti, Paris. (I'm not taking sides, just remarking that it's an important difference)

@OwenReynolds: Except in a few subject areas, the accreditors do not look at the contents of the curriculum, only that it is mostly controlled by experts.  Even in subject areas where accreditors look at the curriculum, their minimums are usually quite low.  The geology accreditors want there to be more geology professorships, and there are more geology professorships when there are more geology students, and there are more geology students when all potential geology students are held to standards they can meet with reasonable effort.

Just one example to further illustrate differences: Not many books are banned in France. In recent times, I think, only « Suicide Mode d'emploi » ("A Guide to Committing Suicide") is banned. Bans are concerted decisions made by the Ministry of Education (occasionally challenged by the highest court in the country). By contrast, if you google for "banned books in U.S. colleges" or similar, you get multiple stories for each U.S. state. I'll copy an example in a separate comment.

One random example from Idaho: "The bill also appears to ban the use of primary historical documents detailing the history of hate groups such as the Ku Klux Klan, including documents from the organization itself or its leaders or adherents; books by major historical figures such as Adolph Hitler’s “Mein Kampf;” and other works written throughout history by those who have advanced the philosophies of hate-based movements, even for use in studying their history, causes or prevention." (https://www.idahopress.com).  There are many such examples, even in California where I live.

This is a minor point in your interesting answer, but I think it's worth noting that France is not the only country ( even in Europe)  that considers headscarf as an issue when it is worn at school by teachers or by young students ( headscarf is allowed in universities in France). This religious sign is banned in public institutions in Turkey, for example. There are deep reasons for that, rooted in history.

@FloridusFloridi, Other countries have similar bans true. Note that in Turkey the ban was relaxed under Erdogan. And also note that the French law applies to all "public" places, public in the broad sense, that does include all universities and schools, both public and private, the only exception being places of worship. [I just checked the French wiki to make sure]

In my experience as an American student, the overlap depends heavily on 1. how good your high school is and 2. how good the college is. There is a huge range in the academic rigor of high schools and colleges. Public schools depending on region vary widely in how many advanced courses such as AP courses they offer, some only one or two, others 10+. Top level public high schools and good private high schools will already overlap with basic undergrad curriculum, and very good private schools already teach college level material. I went to a good public high school in a relatively wealthy area which had students who performed decently well at highschool olympiad type competitions and had one or two advanced classes taught by people who also taught at local colleges. Highly selective colleges will be much faster paced and expect much more math background, for example the first year undergrad math courses teaching set theory and combinatorics may already be more advanced than all of community college's math courses.
One important difference I noticed is that college gives much more independence in terms of homework. Most of my college classes had assignments given once a week and most professors did not care if you showed up to lecture or not. My college homework required much more independent thinking and persistence in solving problems, for example each math problem in one homework may take me anywhere from 0.25-10 hours of total time thinking and experimenting, while I would rarely spend any significant time on any one high school problem.
Some colleges let you "test out" of introductory courses if you have a certain score on the corresponding AP exam (usually a 5, the highest grade, sometimes a 4) or have credits from taking a course at a local college already. This varies widely depending on college and even between different majors at the same college. You might expect more selective colleges would be less accepting of AP credit, and this is true in some circumstances but doesn't hold in many others. My university, which is well known for its CS department and intro CS course, let students skip different levels of the intro CS course depending on if they got a 4 or 5. (They also had a placement test that I took to try to skip the intro class, but my personal gripe is that it wasn't written well with typos and it tested Java, for which I had no experience.) For some AP exams I got credit for the minimum major units but it didn't fulfill my major course requirements.

I think I have heard that you can "test out" of entry-level college courses (I think by having high school advanced placement grades and/or performing well in admission tests); that is, if you are good enough you almost skip the first semester. Can you confirm that? That would be part of the overlap in course material the OP is observing.

@Peter-ReinstateMonica Yes. I added some detail to my answer. If you have any other questions I can try my best to give you my experience from applying and attending

They may use the same books, but college is about twice as fast as high-school. A year-long high school "AP computer science A" course tests out as a semester-long college computer programming-I. In practice, it's a little less (the high school version covers as many topics, but they write fewer program so are a bit weaker overall). I think high school chemistry is the same way.
The hours work out. The rule was that for a difficult college class you'd have 6-9 hours of homework each week, whereas -- I don't know this as well -- high school is a lot less.
It's understood that 1st year college classes can often be tested out of or handled with some sort of transfer credit. It was (probably still is) common to go to a nearby community college, transfer those credits, and come into college as a 2nd year student. That's when you get into the subjects that no one else teaches except a university.

AP Computer Science A may be a bad example. I've just looked at the 2021 curriculum, and it's still a joke. A typical Intro to Computer Science class at a university would cover that content in a couple months. There's a reason it's the only AP course that my university wouldn't give credit for.

AP Computer Science once had an AB test which covered a little more material (stacks, pointers). However, AP CS AB enrollment fell, esp. among minority students -- so they changed AB->A to fight that decline: https://www.edweek.org/policy-politics/college-board-intends-to-drop-ap-programs-in-four-subjects/2008/04  In truth, this was a small change since "B" material was often covered in a few weeks. Your idea of a typical CS intro seems biased: top CS schools often use Structure and Interpretation of Computer Programming (little overlap w/AP CS) but that is not like the intro at most schools.

@AndrewRay I suspected as much but my time reviewing transfers was before that course existed locally. To your point, going 1/3rd or 1/4th as fast makes it an even better example of my "HS may look the same, but it goes slower" thesis

@kurtosis You're right that it is secondarily true that aside from being very light on content, the AP CS A curriculum is spectacularly bad, with whole units on Java-specific concepts like ArrayList, immediately followed with a unit on 2D arrays, which I hope is all about how you should never use them in Java, though I doubt it. It even dips into ethics and intellectual property in the middle of the unit on iteration for some reason. However, while the AP CS A curriculum doesn't line up well with a real CS intro course, that just makes it even more of a joke.

@kurtosis Hmmm...my read of that is that High Schools used to try to have a course that ran at the same speed as a college course, but it was cancelled for low attendance. Probably because it ran too fast. My understanding of the other half is that CS-Principles was created to get non-white males interested, and did that very well

No idea about CS Principles. I don't think there is a big difference between the material in A vs AB... IF CS A is taught by a smart+aware instructor. I know somebody taking CS A and they are not jumping around to unrelated topics -- maybe because they already covered ethics etc. in a prereq and did scheme as in SICP (DrRacket, but basically scheme) in another prereq. So while CS A may not line up with what we have seen as intro CS, that doesn't mean it differs markedly from CS AB. My questions to the student I know suggests they covered most of what I covered in AB.

It's going to depend on which math and physics books you're looking at.  There are typically several levels of 1st year college courses.  First year calculus, physics, &c for liberal arts or business students are not the same courses as those intended for STEM majors.  If you're looking at texts intended for the former, they probably do cover basically the same material that would be in the high school courses that students interested in math & science would take.
For example, looking at my local university's online catalog, there's "MATH 176 - Introductory Calculus for Business and Social Sciences" and "MATH 181 - Calculus I" for STEM students.  Both of these require either passing some of the 20 or so basic math courses, or a sufficiently high score on college entrance exams.  (ACT 28 or SAT 650.)  Most people intending STEM studies will have taken those basic math courses in high school, and will have the necessary scores.
MATH 176 is a 1 semester course, and except for perhaps a statistic course, the last math course those business & social science students will take. MATH 181 leads to MATH 182 & 183 the next two semesters, then differential equations &c.
Likewise, we find General Physics I & II for non-majors, but Physics for Scientists & Engineers, General Chemistry vs Chemistry for Scientists & Engineers, and so on through all of the sciences.

The content doesn't differ between advanced high school courses and college courses, but the pedagogy and evaluation techniques do.
For example, when I took AP biology and calculus in high school, they were taught over the course of 2 or 3 semesters, and the grades were based roughly 80% on attendance, homework, and regular quizzes, and 20% on mid-term and final examinations. Classes were mostly lecture, but also included in-class work, where students could get familiar with the content and receive help from the teacher. The teacher was concerned with each student succeeding.
In college, the classes which teach this same content are taught over the course of a single semester, with the evaluation criteria basically flipped: Grades were based roughly 80% on mid-term and final exams, and 20% on homework. Classes were completely lecture, and while the instructor wants you to succeed, the burden is on the student to ask for help when they need it. Another difference is that these classes were often accompanied by companion "classes", such as twice weekly recitations (where a graduate student would help a 20-30 person subset of the lecture class, without a separate grade), or labs (focused on experiments, graded separately).
*This is an anecdotal answer based on my experience as a millennial growing up in the US, going to public schools and a public R1 university.

There are several differences between the two systems.  It might be helpful to think of the first year of American colleges as weakly like the college preparatory courses in France.  I say that because there is some attempt to even out the pretty substantial disparities among state educational systems.  College in the US is one year longer than college in France.
For example, my cousin was from Louisiana when he went to college.  Because they require both French and English, they do not require students to take four years of English.  That can be an insurmountable barrier to a college that requires a student to have four years of English to be admitted unless they voluntarily took extra English.  Some community colleges use that first year to teach deficiencies, although these are often "zero credit" courses.
Also, most, if not all colleges have a mission.  It is usually a population they are designed to serve, but not always.  We have local community colleges and tribal colleges that are designed to serve the college educational needs of the local population.  They are a good choice for many students because they are adapted to the local education systems.  They transition students from the local public school system to that which is expected from a person with a degree.
In addition, we have a system of private colleges and universities.  They often have a different mission than the public colleges and universities.  Quite often, they are as concerned with the intellectual and moral formation of the student as a reasoning adult as they are with conveying content.  There are also private technical schools that provide narrow education and are focused on a single professional group such as engineers.
Intermixed with these are the research institutions.  They are usually doctoral granting colleges and universities.  They can be extremely rigorous and selective institutions or they can have a community college component where they transition students from the local educational system to research level education.
Also, although small in number, there are a number of military institutes and academies.  They exist to train the future officer corps for both the state and national military systems.  They are often elite institutions.  The U.S. Naval Academy, based on post naval career outcomes, is probably the nation's number two or three school.
Finally, there are the Ivy's and the Public Ivy's.  They are the place where the children of the wealthy who are at least slightly talented meet the nation's best and brightest.  About a third of the students are "legacies," the children of alumni.  They get in because their parents or grandparents or great grandparents got in.  Admission is a combination of wealth and talent.
Another factor is the difference in the goals of the French and American educational systems.  Except for technical education in American high schools, the goal is to teach a little of everything.  The education is general and only focused if the student chooses to focus it.
So, to try and answer your question as to why some college textbooks are similar to high school textbooks, the books fill a need.  Some students enter college with two semesters of calculus, an extra year of chemistry, an advanced English composition course, and an advanced biology course.  Others are struggling with math, English, and the sciences.
America is very uneven and very unfair to be born in.  Without being here, it cannot really be explained because of the size and political differences.  There are places in the United States without running water, sanitation systems, or electricity.  There are states that still rely on "one-room schoolhouses," where all grades are taught at the same time by one teacher.  That teacher is teaching first grade and twelfth grade in the same room.  There are places where the teacher does not speak the same language as the students. There are schools in the US that don't have books because they cost too much.
Sometimes in the same town, there will be a public school where students are required to turn in their science lessons in virtual reality modeling language.  Some schools have robotics programs. Some high schools offer college classes in their building alongside high school courses.
American colleges are the last chance for the students who have the greatest disadvantages to be given the opportunity to catch up with the most privileged.

I find your third-to-last paragraph a little hard to swallow. I'm sure there are cabins in the woods without water and electricity in both the US and France, and I fail to see what they have to do with education. I would be surprised if there are schools where the same teacher is teaching first and twelfth grade in the same room (and if that happens in some faraway place in Palau, I would expect similar in some French DOM/TOM), much more if entire states still "relied" on this, suggesting a widespread policy. Can you add a few links?

@Stephan Kolassa: OTOH, having grown up in a place that approaches the (rather exaggerated) extreme of that paragraph, I pity kids forced to grow up in urban areas.

@StephanKolassa I live in Montana.  We have a huge number of one room, one teacher schoolhouses.  We also have a large number, certainly in the tens of thousands, without access to running water, sanitation or electricity.  As to where they exist, here is a link.  https://billingsgazette.com/one-room-schools-these-kids-are-getting-a-fabulous-education/article_55347748-26ee-5226-8dbe-850c9df337a3.html  The article says there are over sixty, but I was reading a report that said there were still 88 although that was five years ago.

@StephanKolassa As to housing quality, I have another from Montana, although you can also get the same in the American southeast and on many reservations.  https://www.greatfallstribune.com/story/news/local/2016/03/31/crisis-backyard-montanas-reservation-housing/82466032/

@StephanKolassa I think the paragraph is a fair enough description. The U.S. is probably more diverse than even the E.U. Add to that the fact that schools are substantially funded by local property taxes, and the discrepancy between the good and bad places leads to a big overlap between elite high schools and sub-par colleges.


text:
Should Thank You Cards be Written After an Acceptance or After an Educational Experience's Conclusion?
Circumstance:
Recently, I received acceptance to a Certified Nursing Assistant training program and I plan on writing thank-you cards to the program director as well as each faculty member.
Question:
Should I have written the program director a thank you card immediately after she extended an acceptance to me or shall I wait until the conclusion of the program?
Thought Process
My reasoning is if I did the former all I could thank the program director for is the acceptance and possible future benefits and opportunities as a result of my completion of the program. Whereas, if I wait until the program's conclusion, I could mention specific skills I learned during the program.
Therefore, when I compose my thank-you card it might come across as more sincere and meaningful.
What is the convention/procedure on these sorts of things?

Don't know about a thank you card, but in my opinion it is totally ok for the students to chip-in and jointly buy the lecturer a bottle of fine single malt. After the final exam has been graded, that is. It is a mystery to me why my students never realized this.

I doubt that most of the faculty members had anything to do with selecting the applicants for a fairly low level and short (12 weeks or less) course. It was probably mostly a box-ticking exercise by the admin department. Sending "every faculty member" a thank you card for being accepted seems faintly ridiculous IMO.

@aleph I assumed they meant each of their instructors

For what it's worth: my reasoning would be exactly the same as what you write under thought process. I also believe that the recipient would appreciate getting such a card. As for convention (the actual question) I think the answer by Bryan Krause gets it right. But that of course makes it only more of a nice surprise for the recipients if you do write them.

I don't believe it's necessary to write any thank you cards in this situation.
It's fine to thank someone who goes above and beyond or has a particular impact on your education, but I don't see that here.
A brief in person "thank you" is okay, but also not necessary.
It's also fine to say thank you as you accept. A card seems overboard.


text:
Is an undergraduate physics degree the same everywhere in terms of coursework?
Is a degree in physics the same everywhere in terms of what is being taught or are there differences from one institution to the other ?

Why would you expect every school to require the same curriculum?

There are not only differences between institutions, but also within institutions. For example, at MIT "The Physics Department offers two different programs leading to a Bachelor of Science in Physics, giving students the opportunity to tailor their study of physics to their individual career goals. The focused option is an ideal preparation for those students who plan to go on to graduate school in physics or a related field, while the flexible option provides a strong background in physics for those whose career paths may not include graduate work in the discipline." while at UPenn there are 6 tracks.

That, is not good ... gulp! (unless you are @MIT)

In the UK, undergraduate physics degrees have to be accredited by the Institue of Physics to ensure they all teach the same material at the same standard. Of course, there will be deviations and differences between courses, particularly in specialist modules or research-based components of the degree.
This may vary depending on the strengths and weaknesses of the department in question-- for example, in my undergraduate degree I did a lot of solar and stellar physics (at least 3 different modules across my 2nd and 3rd years) because that was a strong research group in the department. However, I did the bare minimum of particle physics because no one in the department had expertise in that area and therefore there was only one module on it in the first year of my degree.
While this answer focuses on the UK, I expect the same is broadly true in other countries, except perhaps those which do not have a particularly high quality or standardised higher education system.
Physics as a subject is generally easily standardisable, as many concepts build upon previous knowledge (e.g. going from classical to quantum mechanics) and therefore all physics degrees will follow broadly the same structure. Contrast this with history, for example, where one could specialise in the Cold War period from almost the beginning of a degree, without needing to know and understand the intricate details of everything that has happened in human history from the Neolithic period onwards.

"except perhaps those which do not have a particularly high quality or standardised higher education system." — Countries lacking a standardized higher education system of course includes the US.

There're a lot of similarities, and also differences. My experience is that some topics are core and every program covers them, while others depend on whether the department has people familiar with the field and / or are electives. Examples of the former:

Newton's Laws, vectors, conservation of momentum, moments of inertia
Laws of thermodynamics, definition of temperature and entropy
Basic particle physics (the kind that can be memorized, e.g. "how many quarks are there?")
Schrodinger's equation, commutators, expectation values
Maxwell's equations, vector calculus
Angular momentum in quantum mechanics

Examples of the latter:

Relativity (bit of a shame, but it is a hard topic)
Astrophysics
Cosmology
Quantum optics and information
Advanced classical mechanics (Poisson brackets, Lagrangian mechanics)
Electrodynamics
Particle physics (the kind that requires calculations)
Biophysics


text:
Am I violating authors copyrights?
I simplified a publication into a method scheme and then published it on ResearchGate.
I added a reference to the original publication in my method paper.
My question is: am I violating the original authors rights by publishing this method paper I wrote online?
You can see the paper here: Ibuprofen RP-HPLC Method.
Thanks :)

I Got 2 down votes, I don't know why and it's my first question on Academia St. Ex. .. Am i doing something wrong?

I didn't downvote, but the formatting of your question is a bit jarring- the random bold text and capitalisations don't add anything to it. (Plus in English, I (the pronoun) is always capitalised.)

@astronat okay, I'll avoid this mistakes next time.

In general, information is free, but its creative expression is not. Therefore, you can build on other people ideas from copyrighted works but you can't copy text or images from such works.
Therefore, you can freely summarize other people's methods, provided that you cite your source - and that's an issue of intellectual honesty rather than a copyright issue.
However, you copied verbatim the whole paragraph in your "Sample preparation" section instead of explaining the method with your own words. This can only be done if it qualifies as fair use (or equivalent rules outside the USA) or you get permission from copyright owners - be it specifically to you or with a free license.
Since the original article states that "This is an open-access article distributed under the terms of the Creative Commons CC-BY-NC 3.0 License" (link mine) you can copy it while abiding to the license. You are obliged to:

Acknowledge authorship of the copied fragment. It's debatable if just citing the original work without stating that you copied text from it is enough.
Not to make any commercial use of your paper. For example, you can't publish it in a commercial journal. I would say that publishing it in ResearchGate doesn't qualify as commercial use, but the limits of commercial use are tricky.

If these conditions pose a problem to you, or even a slight nuisance, you can try to remove the copied content and explain the same ideas with you own words. This way you can get rid of copyright and license issues and you will just need to keep citing the original paper.
Addition
The original article is also published here under the same license. This publication is more specific about obligations of reusers of content, with a dedicated page.

I would argue that publishing it in Researchgate is commercial use. They have ads. They make money out of it. You gave it to them and unlawfully authorized them to redistribute it and make money with it when you clicked "publish".

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


text:
Does a conference poster count as a publication for PhD application?
I'm preparing a CV and required documents for PhD applications and I've been asked to provide references to publications. I've been wondering if it's appropriate and a good idea to put my student poster there?
The field is Computer Science and the poster has been presented during one of the top conferences. Posters were not part of proceedings and are not officially available (only online abstracts).

It's definitely a good idea to include such a poster in your CV or mention it elsewhere in your application (e.g. discuss it and the work in the personal statement). However, I would refrain from listing anything under "publications" unless it has been peer reviewed and published in a reputable journal.
I think in this particular case, the application is asking for references to papers rather than posters, but it may be worthwhile emailing the admissions people at the department to ask where you should include the poster.

"in a reputable journal" - In computer science, posters are often submitted together with a short paper, which is included in the conference proceedings. This would count as a (small) publication as well. But this case doesn't seem to apply here.

Thanks for the response! I'm thinking about putting it in CV under "Presentations", together with conference talks without peer-reviewed papers.

@thorek A separate section is probably a good idea.

It depends on the context, more specifically:

What is the importance of such a poster in relation to your total list of published works? Do you believe that it was one of the top studies that you did ?
Is there any in progress work that you are doing for expanding the work on this poster that you would like to cite in your application ?
How relevant is this conference to the field you are applying ?

In my case, in my MsC application, I included my two conference posters in my CV as I did not have any relevant journal publication accepted at the time of the application. I would recommend using a different section for this, such as Peer-Reviewed Publications and Conference Presentations or Conference Proceedings. However, if you believe this is a minor work compared to what you have already produced I would not worry about that.
Lastly, I agree with @astronat that may be worthwhile contacting the department to ask what they are looking for in the application and how you could include this work to improve your CV.

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


text:
Feeling lost as a PhD student
I'm a first year PhD student in theoretical physics. My problem isn't strictly due to imposter syndrome, but rather not knowing how I should be spending my time. My supervisor has only given me some vague guidance on what my project should be about, while I hoped to be given some reasonably well-defined first problem to work on. His most concrete suggestion was along the lines of "go study some lattice model on this particular class of lattice geometries and see if you find something interesting".
For the past two months, while trying to follow his suggestion, I have been attempting to learn various methods that might be useful to my project, allowing me to study said models in said geometries, or to at least gain a better understanding of the available literature, but that's not a way to continue; there is not enough time to learn even a handful of methods that would be relevant to the problem at hand in sufficient depth. I've only had a couple of ideas of how I might be able to study the problem emerge during this process, but even then I don't know  if those ideas are feasible, let alone sound (and the more I think about them, the less sound they appear).
My supervisor isn't actively doing research himself, and only engages with the research being done by the people in the group through meetings, which is unlike some other group leaders I have done projects with. I appreciate that my supervisor gives me full independence in choosing what I want to work on, but identifying a suitable problem to begin with and means of solving it is what I struggle the most with. Other PhD students in my group are lucky to have co-supervisors who seem more engaged with their projects, or had been supervised by a postdoc during their Master's project and now have some clear follow-up problems to work on with their postdoc partner.
Is this how PhD research is expected to look like at the beginning, or are those signs that my supervisor is not particularly good at supervising? I'm in the UK, so changing my supervisor is not an option.

I won't say that changing supervisors is completely out of the question in the UK. I've known of several students change supervisors.  It is, however, regarded as fair big step, and its not guarenteed that the department will agree.

Does this answer your question? How should I deal with becoming discouraged as a graduate student?

Despite the added UK tag, I don't think this is special to UK in any way.

I went through a similar phase then "Boom!". Similar phases happened to many PhD students I met. Take this as a bit of optimism.

@Buffy since PhD students in the UK have a supervisor and thesis title from the get-go, it's harder to change them, unlike systems in which a student is admitted to the department and shops around for a topic and supervisor. Part of the question is about changing/adding supervisors, so I think the tag is appropriate.

@astronat FWIW we have a supervisor and a title from the get go in Russia as well - doesn't mean changing one is hard. Potentially lost time is more of a concern than formalities.

I don't know if it's the field, but I've heard this story before in UK theoretical physics.
Perhaps it might help to be able to go to your supervisor for specific advice. You said you've been trying to learn lots of methods that might be useful to a sufficient detail to use them. That sounds inefficient.
I have to admit, I'm not a theoretical physicist, but what I'd do is make a list of all the models you can find in literature in the specified geometry, and see which one excites people the most, or seems to have the most open questions. Or hasn't been studied at all.
Then I'd make a list of all the methods that you could apply to it - learn just enough about each one to be able to be 50-60% confident it could be applied and no one has done so before. Then pick one method.
Does (did) your supervisor specifise in a particular class of models/methods? It might be worth finding a combination that is complementary with someone else in the dept. Like if your supervisor has worked with model X, and your list of methods includes a method that someone else inthe dept has experience with, that might be a useful combo. Congratulations, you've found yourself a co-supervisor.
Then write to your supervisor saying "here are all the models I reckon I could study, and here are the methods I think might be applicable. I think perhaps I might start by trying method X with model Y, can we arrange a meeting to discuss if you think this is a productive way forward?"
They might say "no I don't think this model/method will be productive", in which case be prepared to say "what about this other model/method" or "which of this list of methods do you think would be more productive"?
He might just shrug, and say "go try, see what happens".
Again, discipline specific considerations apply, but usually, if you apply a particular method to a particular problem, and do it well, it can form part of your thesis even if it doesn't work.

Firstly, there is always the option to change your supervisor, even in the UK. However, that may be the last resort option, and you have other avenues you can explore first.
Have you tried asking your current supervisor for more guidance? If you don't tell them that you feel lost with your current project, they won't know! You can write them an email explaining things just as you have done here, or ask for a Zoom meeting or in-person meeting if you would prefer to talk face to face. Communication is key! The supervisor-supervisee relationship works best if you can both talk honestly and sincerely with each other from the get-go. It's not too late to explain your feelings and problems to your supervisor. (It's also not unusual to feel lost at the start (and middle, and sometimes even the end) of a PhD, but it sounds like in your case you have had a particularly scant amount of guidance.)
If your supervisor is unwillingly or unable to give you more help, you should be able to officially or unofficially add a second supervisor to your supervisory team. In fact, I'm surprised you don't already have one -- at my university it was mandatory, to avoid this exact situation. Ask around amongst those keen and engaged postdocs to see if any of them would be willing to take you on as a student, or unofficially mentor you and provide you with some guidance. Make sure that you let your current supervisor know that you are doing this, rather than springing it on them once all the arrangements have been made.
Finally, if there's no one in your department who can help you out as a co-supervisor, you could consider starting a collaboration with someone from another university. This is likely to be quite hard since you are a new PhD student with presumably not much of a network. My advice is to to go to conferences and workshops in your field and get talking to people who are working on interesting problems. Suggest something that you could work on together, if you are able to come up with an idea (not always easy!). There are also other questions and answers on this site about how to start new collaborations.

Talk to your supervisor
Supervisors are there to help, so if you feel that you need some more specific/detailed guidance at this stage of your program, go and see your supervisor and have a talk about it.  You can let him know that you are having trouble with the general task you have been assigned and you think you need some more detailed guidance on how to proceed.  Research expectations are not high for a first-year PhD student, so it is likely that your supervisor will be willing to accommodate some additional guidance to help you develop.
Most major problems that arise in supervision of PhD students occur when the student has a problem, or is not making progress, but they are too shy or anxious to speak to their supervisor about it.  Effective supervision requires the student to be realistic about their situation and progress, and report candidly to their supervisor about any difficulties they are having.  When this occurs, supervisors can usually assist the student and nip initial problems in the bud.


text:
Can there be context rich problems in Biology?
Context-rich problems are short realistic scenarios giving students a plausible motivation for solving the problem.
As we search research literature, one can see lots of research in context rich problems done in physics and chemistry, but we don't see them in biology. Why is this?

Instead of pretending that you are giving them "real" problems, or instead of trying to look like it, why don't you give them really really real problems, like research problems, and let them try to solve it? The fact that none of them will be able to do so is not relevant.

@onurcanbektas, that is probably unrealistic and too frustrating for undergraduate education. Also it would be devilishly difficult to evaluate and assess.

Probably this is because physics and chemistry (along with math) are more often subjects where problems (especially equation-based ones) are often given without supporting context, so educators have put more work into studying now else to approach them.

Perhaps you can start with finding some application of biology in real life that is used to make decisions? I'm not from a biology background, and from my perspective, I cannot find any examples where my decision is heavily influenced by my knowledge in biology.

@Buffy Assigning research problems to undergraduates in a classroom setting is ubiquitous in the humanities.  It's not unrealistic in general.

I'm not familiar with biological pedagogy, but I don't believe the premise of the question.  I'm sure some biology faculty do this.

@Buffy Maybe for math, but not for Science subjects


text:
Should I add the award of a Graduate Research Fellowship to my CV before I start it?
I have been awarded a Graduate Research Fellowship from the grad school I intend to attend. It will start in Fall 2023. Should I add it to my CV in advance?
If yes, how should I mention it there? If no, why do you think that?
Thanks in advance.

If you add it, list it with dates so that it is clear to readers. You can say "... beginning Sept. 2023", or "forthcoming" or similar.
The only real issue is being clear.
But, I wonder why you need to do this if you've already accepted a position. Your CV isn't going to be used much, I'd guess, in the short term.

There is no specific need of this in my CV in this short period of time, Professor. It's just, I update my CV pretty frequently. I try to keep it as updated as possible.


text:
Teaching Robotics to Mechanical Engineering Students Vs Electrical Engineering Students
My background is in electrical engineering. I have taught robotics to electrical, electronics and CS students. This time I have to teach robotics to mechanical engineering students. How do I keep the interest level high in the class?
I am afraid the concept of programming (microcontrollers), and electronics will lower their interest. But I think programming is a must for them as well.
Any suggestions how to proceed, go in depth, and keep the interest level high? Should there be much difference between the syllabi of the two trades?

Does their ME curriculum require them to have had any programming before this? Or is this the students' first exposure? That will largely determine the way you approach the course, but even in either case you should probably expect their ability level to be lower than EE, CE, or CS students.

Are the ME students at your institution required to have exposure to any EE/CS topics that would help them in this robotics course? (At my institution, ME students must take several relevant EE courses, so I would expect those students to be well-prepared for a robotics course, even though we don't offer such a course.)

What level are these students, BS 2nd, 3rd year? During my undergrad (in ME) I did a lot of controls courses (and I think this is common in ME programs), so framing the programming around control would make sense. In general, teaching new skills focused around a use-case is more motivating than teaching it for its own sake.

You could focus on the kinematics and classical mechanics of robotics, particularly in anthropomorphic robots such as robot arms and human analogues. A good example would be the inverse kinematic equations required for translating end effector position and orientation to revolute joint angles. That can cover things such as Devanit-Hartenburg models and numerical vs. analytical solvers.

The problem with your proposed approach is that OP may not have the background to confidently and effectively teach from the classical mechanics angle.

@Mad Jack some of the stuff I mentioned isn't particularly advanced, if OP has a decent mathematical background they can probably learn it themselves after a little self-study. They can avoid mentioning more complex things if they aren't confident.


text:
How can I convince my supervisor that I have enough data to support my findings?
I am a final-year Ph.D. candidate in a physics-oriented field. Over the course of my program, I have developed a postulate which leads to some contradictions with some of the tenets of my field, and I have obtained what I would consider a suitable amount of data which both supports my postulate, and conflicts with the (pre-)existing conclusions.
I am in the process of writing a paper on the matter with my supervisor. While initially supportive of my ideas/work, he has unfortunately seemed to change his mind recently, for a number of reasons which I find questionable. Of note, he has repeatedly stated in writing that the work is unsuitable, because I have failed to "either prove that the postulate is correct, or disprove the existing work" (according to further discussions, he believes that having conflicting data is not proof that the existing work is incorrect).
However, in my understanding of the scientific method, it is not possible to prove that my postulate is correct, or that the existing work is strictly incorrect. As I understand it, all I can do is provide data which agrees with what I am trying to say, and which contradicts with what other work has concluded. While I believe that I have done a sufficient amount of work necessary to support my thesis, he is of the opinion that I haven't, and is threatening to withhold granting my degree if I don't meet his expectations.
Perhaps related: he is an engineering professor and as far as I can tell has not published on a postulate before. However, to be fair, neither have I!
My questions are then:

Assuming I obtained the data in the best possible manner, is my supervisor correct in that I have not reached the required threshold for my work to have suitable academic merit necessary to receive a doctoral degree? (Generally speaking - I am aware that practices may vary depending on location).
If not, what must I do in order to reach this threshold?
If so, what can I tell/show him in order to convince his that my work is indeed suitable?

I don't think that anybody can possibly provide an answer without having access to many more details. The precise field matters, how well established the prevailing theories in your field are, how the quality of your data compares to previous work, how the rigor of your arguments compares to other work, etc.
Generally, making these sorts of judgements is what your advisor is for, because he/she has many years of experience in the field.
Now it can happen that your interests and those of your advisor are not perfectly aligned. Your advisor may be too conservative, because he/she does not want to make a mistake. You may be overly aggressive, because you want to get your thesis done.
The question is how to proceed. You could ask your advisor to let you finish a draft, and show it to a third person, an expert in the field (possibly a member of your thesis committee) with no direct interest in the outcome, and who you can trust to keep a confidence.

Agree that an outside perspective is needed here, that is what thesis committees are for! @ConfusedPhD101, has OP assembled a committee yet, or gone through the thesis proposal? The committee members may have constructive suggestions, and, if they are on your side, are better placed to apply peer pressure to your advisor.

You are right about the scientific method.
We cannot comment on the evidence you have not provided.  In general, you can demonstrate that evidence is sufficient to disprove a theory with statistical tests.
In physics and related fields, disproving one theory and proposing an alternative is not usually sufficient to obtain a PhD.  For tabletop experiments, you would normally conduct at least three related experiments which test different theories.  A theorist would develop three related theories.  Customs and student achievements vary.
You should have a dissertation committee and you should consult all of them about the quality of your work.


text:
Politeness of a follow-up E-Mail regarding administrative task
I have to get a certain document filled in by a professor in regards to my major/curriculum.
Initially, I reached out 3 weeks ago, and she instantly replied that she'll be happy to do so, and asked for some other information she needed. I replied with the information instantly, but didn't hear back, unfortunately.
10 days ago, I therefore sent a follow-up in the following form:

Dear Professor X,
I was wondering if you've had the time to look at  I sent already?
  Thanks!
Signature

Since I still haven't received any reply, I was thinking of sending another follow-up of the following form:

Dear Professor X,
I hope you've had a good weekend.
I was wondering if you had received my previous E-Mail?
Thanks!
Signature

Would this be polite enough? (For some reason it strikes me as a bit too straightforward, but on the other hand I don't really have any reason to add an apology either, I think.)
I actually encounter such situations regularly, but my follow up emails always look more or less like the above, sometimes with an apology for reaching out again, even if I think it makes the E-mail look much too submissive. So I'm basically wondering if it is appropriate to send follow-ups in such a format.
I just wouldn't know what else to say in them, since the whole point is just to get the target's attention again if they accidentally missed it, were too busy, or forgot about it.

Professors appreciate it when you 1) tell them what you want, 2) tell them why you want it if not already obvious, and most important, 3) tell them what the deadline is.

It may be time for a phone call.

Rather than just asking if they received the previous email, reiterate what it is you're asking about, why you're asking them specifically, and include a deadline. This saves the recipient from having to trawl back through three weeks' worth of email to find your original request. So, you might want to send something like
"Dear Professor X,
Is it possible for you to fill in this form that I need for [insert reason here]? I'm asking you because [insert reason here]. The [admin people/ university/ department] need me to send it back to them by [deadline]. I've attached the form to this email.
Thanks in advance for your help!
AnotherStudent"