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Is my PhD supervisor contributing too much to my project?
I am a PhD student in pure math, now in my second year. I understand that different PhD supervisors have different levels of involvement with their students' projects, and I very much appreciate how engaged my supervisor is with what I am working on. However, there is something that concerns me regarding whether the input my supervisor has is appropriate.
He is mind-bogglingly quick and can sometimes outline proofs of new results during our meetings, which I then spend days making sense of, writing up properly in full detail, refining arguments where necessary etc. Sometimes he sends me notes via email containing unpublished results, with very little context. I do not ask him to do any of this, however I am very grateful for his help. Is this type of input unusual?
My main concern is that when writing up my thesis I may have to add in lots of disclaimers such as 'this proof has been communicated to me offline by...' to acknowledge that the original idea is not my own. Would this look really bad? Also, some of what he has sent me are results that I likely would have been able to do by myself given a bit more time, but I cannot demonstrate that now because he has beaten me to it.
Communicating my concerns to him is tricky because in my experience he does not respond well to questions unless they are of a strictly mathematical nature and I do not want to appear ungrateful for his efforts. Any suggestions or advice would be much appreciated.

"My main concern is that when writing up my thesis I may have to add in lots of disclaimers" - regarding this specific issue, will a stapler thesis be appropriate in your field/institution? In that case, most of the "meat" of the thesis consists of published or publishable manuscripts, which can be coauthored; you don't have to outline the specific history of every line of work in a coauthored paper, just cite it as "Student and Teacher, 2022".

@BryanKrause I'm not familiar with this type of thesis and am unsure if it is allowed in my department. My field is pure math and most PhD theses I have seen from my department are 50-100 page texts of as-yet unpublished material, although many students do end up making a research paper or two from the contents of their thesis afterwards.

@BryanKrause, stapled theses are uncommon in math.

Yes, he is probably doing too much. Of course, he has more experience in the field than you do, so can see solutions more quickly. It is hard to say what to do, unless you think it would be safe to have a conversation and let him know that you need to struggle a bit more in order to improve your skills.
But, you could also set his suggestions aside and work on the problems/proofs/whatever yourself until you reach a conclusion and then review them.
My advisor was probably able to write my dissertation much more easily than I could and one of the major proofs in it was his, since it had the potential for expanding insight (my proof was more standard).
But, if he isn't trying to steal your thunder, then it really doesn't matter if he has a proof before you do, unless he publishes it. If he is doing his job properly and guiding you then you will be first to publish. It is, however, much better that it is your own work that gets explicitly represented in the dissertation. And other people, unknown to you both, might also have had those insights first but didn't act on it. (Note Newton's dispute with Leibniz.)
There is a story (apocryphal?) about a professor who was very arrogant who told a (suffering) student "I don't mind writing your dissertation for you, but I'll be damned if I'll explain it to you when I'm done." I don't suggest that this is the situation you are in, but have included it here to indicate things could be worse.
But you would be wise to spend the time to get to where he got to easily by setting aside many (most?) of his hints until you get through the crux. If I remember correctly after more than half a century that is what happened in my case. The professor provided a proof (and I read it) but I struggled to create my own proof as well.
In math, note that it is (still, I hope) uncommon for an advisor to be a co-author on a dissertation, and the work is considered to be your own. But you need to find a way to make it so.
"Doc, I'll never get to where you are if you give me too many hints. I need to struggle through this for my own insights. Thanks."
Good luck. You have the right attitude.

This is very helpful, thank you. I certainly need to force a conversation with him regarding how much he is doing and whether this will cause problems in terms of excessive contribution to my thesis. Would I need to add footnotes acknowledging his contribution to each part or something less specific? He doesn't seem to be concerned about the balance of contributions himself, but nonetheless I definitely don't want to get in any trouble or get too much of an easy ride.

Could you elaborate a bit on "In math, note that it is [...] uncommon for an advisor to be a co-author on a dissertation"? I'm not sure whether I understand what you mean because I've never heard that an advisor could co-author a PhD dissertation (no matter in which field). On the author hand, I've often seen PhD students in math who write some papers with their advisors and some other papers without them.

@JochenGlueck, I gather from other questions here that it happens in other fields, especially when a stapled thesis is common.

It depends what type of relationship you want! On the opposite, there are students who have no idea about how to do something, and of course, their supervisors also do not have any idea where to start.
I have seen way more of the last ones. So I would say that experience beats everything when there is a time related project that has an end: a PhD.
Do not worry about the thesis, accept the input, write, let him revise. His job is to help you to pass and if he actually checks your job, amazing! Some supervisors barely ask for progress, or are happy with everything they are shown because they do not know if it is correct or wrong. Better someone to tell you, that is a mistake.

"Some supervisors barely ask for progress, or are happy with everything they are shown": in all cases I am familiar with, PhD's are assessed by someone other than the supervisor so I would have thought that the expectations of the assessor are more important than that of the supervisor.


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How can I complete the prerequisites for Masters in Computer Science on my own?
My Background: I am an EE graduate, working in a Software Company from last 2+ years as an Application Developer(Java & J2EE). Recently I started thinking of going back to college and do my Master's in CS, as most of the jobs in industry require a degree in CS.
Country of Residence: India
Countries of Interest for University Applications: US, UK, Australia and EU.
I have noticed that there are prerequisites to get admitted to those programs. Specifically, I need to have completed courses in Data Structures, Algorithms, Operating Systems, Theory of Computation, Compilers and Computer Networks. My undergraduate degree did have courses like Computer Networks, but nothing else.
In some other Universities, I can get admitted to MS in CS, but then I need to complete those courses at the College before starting graduate school coursework. I understand all of those things, as I took various Computer Science Courses online. I understand all the things that there are in undergraduate Computer Science Course. So here are my options:-
1) Take a post-bacc Course in computer science. (That Costs a lot in money and Time)
2) Do Nothing and apply without requirements being completed and let them decide whether or not I should enroll in UG CS courses at college.
3) Do some online Computer Science courses on edX, Coursera and show them that.
Which one of them is more favourable to a person working in Software Industry with an EE background?

I had two bachelors in Music and Art, minors in Marketing and CS. I then held a Computer Science career. When I went into the CS Masters program 7 years after obtaining my last bachelor degree, I had several deficiencies. I was accepted with two understandings. (1) I will complete the deficiency courses that are prerequisites to Masters courses I am to take, and (2) my current career in CS demonstrates I have the aptitude to succeed despite my entering the program with deficiencies.
I believe your best option is your #2, to enter the Masters program and complete the deficiencies in your coursework. When you write your letter of intent for application to the Masters program, I would describe these two aspects as they apply to your situation, personality, and drive to complete your degree.
Your other option for the US market is your #1, to complete the deficiencies from an accredited institution, then transfer the completed coursework with you when you apply. You must be careful with this option, to ensure the University you are to apply for a masters with will accept the coursework from the other institution. Before taking the coursework, it is best to call the University to ensure the courses will transfer.
This other option is best if you are under the following circumstances:

Currently working, and can take the deficiencies at night through an online University, or through a local college offering.
You will save money/time from taking the deficiencies from the alternate institute.

Your option #3 will not work, as they require the coursework credit from an accredited institution. Internationally, they usually require a demonstrated bachelors degree in CS. But post-bacc work needs to be completed as previously described.
Otherwise, you are best to just enroll in the University Master program and take the deficiencies there.
When I took the deficiencies for my masters program, I'd take deficiency courses one semester, and then the Masters courses that required the deficiency the next semester. In this way, except for the first semester, I was taking at least one Masters course every semester. Look at the University course catalog to see which courses have the least number of prerequisites that are your deficiencies, and then take those deficiencies first.

New York University offers a preparatory accelerated course in computer science specifically for people in your situation.  Check the "What material is covered in the PAC Program?" section in the link below to see what they expect an incoming master's student to know:
https://cs.nyu.edu/webapps/content/academic/PAC/faq

In the US, it will depend on the school.
At my university they rely heavily on testing for foreign students, because the course on algorithms that is accepted as standard in your country may or may not be comparable to the algorithms course here. This is bad news if you pay a lot of money for a course that doesn't give you the preparation to pass the exam, but great news if you learned the material on your own (or through Coursera, for example) and were able to pass the test.

Maybe you should add your country of residence to your question since this might affect the answer.
In Germany, only 1) would be accepted since all others are not from an accredited institution.
It might be possible to enroll to a program and do all exams in one semester, but you should check this in advance.

Country of Residence: India, And Countries of Interest for University Applications: US, UK, EU and Australia.

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Is being an honors student really worth it?
This is a something I'm really concerned about. I am an undergraduate physics major, and I've been in the honors program at my university for a little while now, and that means certain things. I must take at least 1-2 honors courses (or do an honors-contract in a normal course) every semester, I must make a yearly update to a personal portfolio/e-portfolio, I must obtain a sufficient amount of research-group credit hours before I graduate, and I must defend an undergraduate thesis.
I do like all of this, but what starts to bother me is one other requirement, as well as a few things within the program. We must attend at least one 'Honors Student Council' event per semester (not a big deal, but these are ridiculous/stupid most of the time). Also, most of the other students in the program are snobs and stuck-up compared to other non-honors students. I do like the chance to learn a lot more about the material presented in my classes through honors and course-contracted classes, but I'm starting to think that I could just do that on my own - that is, set that up with professors on my own.
However, I don't really know how useful having an 'honors' distinction on a degree will be. Is it very useful? I've been thinking of quiting the honors program, but I wouldn't want to do it if it will drastically hurt me later on. For example, how much of an impact does having an honors distinction have on graduate school/job applications?

If you're going to do most of the work anyway, why not also do the one unpleasant thing each semester so that you can get credit for the program?

...and I must defend an undergraduate thesis. Is this only for honor students? If yes and you want to apply later for a MSc or a PHD this is a major advantage.

@Alexandros You can get a thesis without being in the Honors program where I'm at. However, the Honors program required that or a capstone where I went.

I recommend an honors student learn that you don't make plurals with an apostrophe.

@ArturoDonJuan I wouldn't quite put it that way... :)

I graduated with honors from the university and from the department I was a major in. I would say it was definitely worth it, especially with research and having the opportunity to be a mentor for two math courses.

Some graduate programs require that you have an honours degree in the field.

It depends on your reasons for being in the Honors program.
Are you in it for the extra line or two you have on your CV or diploma, or the learning experience, or the potential opportunities that arise from your undergraduate institution?
Look carefully at how you've "sold" the Honors College to us. A list of requirements, a mention of a waste of time, and pointing out that you can do everything the HC provides to you without assistance. You come across as dissatisfied with the system.
I am going to try and be as objective as possible, given how I also feel dissatisfied with my time in the Honors program, and be as fair as I can about the situation's pro/cons.
In it for the Learning Experience
If you're in for the learning experience, by all means, it is certainly a learning experience. One of my courses in my Honors program, I learned a significant amount about leadership, and drastically improved my writing skills. I certainly would still have been a terrible writer if not for that class, and that's a plus in my book for how Honors helped me. That being said, not all of the Honors courses are that great. I assume that your program may require you to take classes outside your major to fulfill enrichment requirements. I would recommend you find something that isn't only useful, but interesting. I took a class about the Beatles because it fit my schedule, and that probably could have been replaced with something much better.
For the Resume/CV
If you're looking for stuff to put on your resume, there's probably far more time-efficient and cost-efficient methods. Assuming 1 hour a semester for 8 12-week semesters, plus perhaps 4 hours of other Honors-related stuff per semester, that's about 130 hours of time spent to just add the Honors distinction to your degree. May not seem like many hours, but that's equivalent to 10 credits in a 120 credit degree. Add in the possibility of unrelated Honors courses, and it starts turning into 15-20 credits that could have been spent on other courses. I do not believe you have to be in the Honors program to qualify for Honors-related work, and in fact, I would assume non-Honors students can take your classes anyways.
Potential Opportunities in Research
The thesis/capstone projects provided by the Honors program do provide the ability to perform research projects at the undergraduate level and are likely the most high-yield activities you can get as an Honors student. If you capitalize on this, you should be able to do research in a lab at your university and write, present, and possibly even publish a paper. This is probably one of the few things you can benefit from. If you don't use this, it's a wasted opportunity for sure.
The question becomes whether or not the time spent in the Honors program is worth the additional benefits. After finishing the Honors program, no one asked me "Oh, did you go to the Honors program? Tell me about it." They did, however, ask me about stuff I learned through Honors courses. It's nice to see that I have a certificate for it, but apart from that, once you graduate, whether or not you attended the Honors College matters less than how you capitalized on it.
In case it wasn't apparent, I attended an Honors program in college to completion.

Disenfranchised? Do you mean disenchanted?

Or disillusioned.

@TRiG I went ahead and made the changes with dissatisfied.

Being an Honors student is a prime example of signaling: you could just as well learn the content by yourself, but having that distinction on your degree signals something to potential employers or grad school admission committees. And those people hope that this signal correlates with something useful, e.g., flexibility in thinking, openness to new ideas, conscientiousness etc. (Yes, being able to sit through boring meetings can be a survival skill in many bureaucratic settings.)
It has been seriously suggested that much of higher education is explained by a signaling model.
So you will need to weigh the current pain of boring meetings and uninteresting people against potential future benefits. Your trade-off will depend on what else you could be doing in the time you could free up by de-Honoring.

I personally have profited from being a member of a similar German institution. When I applied for a job in a (mature) startup, one of the founders, who happened to be a university professor, saw this in my CV, and he explicitly said that this helped me get an interview.

Let me add to other answers (this may be a little too long for a comment): depending on what you want to do, you can potentially do things a lot better for your career outside of the honors college.  I was in a similar position, and got "kicked out" of my honors college my sophomore or junior year because I refused to take so many honors courses.  Instead I spent my time taking a lot of advanced math/CS classes (many graduate level), and the honors college director wouldn't let them more than a couple count as honors credit.  (I actually enjoyed most of my honors classes till then, and was friends with a lot of the honors college, including the director.)
I ended up finishing with a dual math/cs degree and a masters in math in 4 years, which I wouldn't have done if I had to spend more of my time taking honors classes.  This was much better preparation for grad school (or many industry jobs).  So I would say it depends on your situation (other answers mention pros of being in the honors college), but if it prevents you from doing other things you want to do, it's not worth it.

I can speak at least for myself in saying that I wouldn't give any extra weight to a resume or graduate school application specifically for going through the Honors program. In an interview, I might learn that some of the specific things you did in your specific honors program do make you more qualified, but I can't really take that for granted just from seeing the line on your transcript or diploma. For example, if you took an interesting/challenging Honors class wherein you demonstrated an exceptionally deep level of understanding in some given concept or demonstrated other useful skills like writing, speaking, teamwork, leadership, etc., telling me about that during an interview would certainly benefit you toward me recommending that you get the position. However, this would be true if you took such a course regardless of whether you completed the whole Honors program or not. The same situation would be true with the undergraduate thesis if you were applying for graduate school. If I read about what you did in your thesis, that would certainly benefit you, but that would again be true regardless of whether you were in the Honors program.
I would also say that this probably varies by field. My field is Computer Science/Software Engineering. My experience in undergrad, at least, was that my university's Honors program was focused much more on humanities than on the sciences or engineering. The vast majority of the Honors courses past the Freshman level were in the liberal arts areas. As such, I imagine that such a program would have been much more useful to someone in those fields than it would have been to me. As far as those who were in engineering, my experience was that the vast majority of the top science and engineering students were not in the Honors program. Among the science and engineering majors, it seemed that being part of the Honors program was much more common among somewhat-above-average students than it was among exceptional students. I can generally tell whether you're above average just by looking at your transcript without regard for whether or not you were in the Honors program, so I don't really gain much information about you just from seeing that line.
You also mentioned that your impression of most of the people in the Honors program at your school were arrogant/stuck-up. This was generally my impression at my school, as well. Since that's obviously not a desirable trait for either an employee or a graduate student, having this on your resume or CV may actually hurt you a bit among those who have had such impressions of Honors programs. On the other hand, it could help you if the person reviewing the resume or CV had a positive impression of the Honors program at their school or of previous candidates who had completed such programs, as Stephan mentioned.

Noting your comments:
We must attend at least one 'Honors Student Council' event per semester (not a big deal, but these are ridiculous/stupid most of the time). Also, most of the other students in the program are snobs and stuck-up compared to other non-honors students. I do like the chance to learn a lot more about the material presented in my classes through honors and course-contracted classes, but I'm starting to think that I could just do that on my own - that is, set that up with professors on my own.
I can imagine this not fitting well with you but to be honest, 30 years on, I actually feel that learning to do the above will be of HUGE benefit to you because:

you'll learn to deal with snobs just like in the working world.
you'll learn patience at doing sub-optimal 'ridiculous' tasks.  Real world training.
you'll learn to to engage, agree, disagree and discuss subjects with other that don't share your opinions.
you'll get to engage with others from widely different backgrounds bringing perspectives you may not have thought of.

Apply these lessons quickly now and save yourself a lot of years of learning them slowly.  You may feel that these are not the important lessons to learn while in higher education but personally experience has taught me the opposite.

I must take at least 1-2 honors courses (or do an honors-contract in a normal course) every semester, I must make a yearly update to a personal portfolio/e-portfolio, I must obtain a sufficient amount of research-group credit hours before I graduate, and I must defend an undergraduate thesis.

An important consideration is that the definition of an Honors degree varies tremendously between institutions. Judging by what you have said, your institution requires quite a lot of its Honors students, but every institution is different. (For instance, the university I currently attend is happy to hand out Honors degrees like candy.)
So no one who is not from your institution is necessarily going to know what that phrase "with Honors" on your degree actually means. If their own experience with Honors degrees is from places that take them less seriously, they won't know all of the work you had to do to earn yours.
Is your advanced coursework, portfolio, and undergraduate research experience highly beneficial for your future in physics? Of course. But if you have done all those things, I'm not sure how much additional value the phrase "with Honors" on your diploma will add.
If nothing else, don't expect anyone outside your university to know how much or how little work your Honors degree entailed.

Depends on how well known your university is in the area.  If your job interviewers are alumni of your school, the "Honors" distinction may carry some weight.  But if you're only applying to places far away or places with people who are unfamiliar with your school, then you're absolutely right

Also, it seems that even the phrase "with honors" has some difference in meaning between institutions. In my experience, most institutions use "with honors" (or its Latin equivalent, "cum laude") to mean that your GPA was at or above a certain level, which is unrelated to whether or not you were part of the Honors program.

I think this has been answered better by the others already, but the Honor's program will open doors and provide opportunities that might not otherwise come your way.  I wasn't in an honor's program but I did graduate with Math and Physics degrees, and unless you're already planning a career in academia, you will need those opportunities.  Just my two cents. :)

At my university the Honors college has a fair amount of money, which supports some additional classes intended for Honors students. In some cases these are only available to students in the Honors college; in others, non-Honors students can take these classes but there is some annoying bureaucracy involved.
If it were me, I would find dealing with this bureaucracy more annoying than sitting through the 'Honors Student Council'. You could always prepare a physics problem in advance and then try to solve it in your head during the meeting.

I've had my older son start in an Honors program only to be annoyed by frivolous and pedantic courses obviously feeding the egos a some Honor professors.  It's these fluff classes that make me want to throw the baby out with the bath water.  Students can and should take fluff classes of their choosing.  Obviously, my older son got out of the honors program; he failed to see the return.
My younger son never entertained the idea - he would manage his own broadening.  Choosing not to go the Honors route actually makes my younger son an unwelcome interloper when Honors students are paraded around as 'better'.  He's taken advantage of all the research opportunities of the fine university he attends, found his set of advisers, and has been remarkably successful as an undergrad and will pursue his PHD at a world class institution - but no thanks to his Department which still sneers at this non-Honors punk ruining their party.
All the pluses for the Honors programs, the third place to grow mind and soul with peers that my son found in clubs and such to some extent but was really denied because he wasn't in the Honors program underscores why he didn't join the Honors program - the very real cronyism and elitism - is distasteful at best.
The fact that he's a student who should be celebrated but is at best tolerated because his success dampens the Honors parade vividly highlights the sense of entitlement of those RUNNING the Honors programs - they expect their students to get all the awards and such - deserving or not.  This isn't a matter of sour grapes - my son landed a dream PHD opportunity where he's been picked up by one the premier scientists in the world in his field. I'm just pissed that he's had to bob and weave his way around these Honors obstacles.
Again I repeat - it is the Honors professors themselves who have the vested interest in their little golden gooses who foist their brand of elitism onto the unlucky 'rest'.  People call the Honors programs meritocracies - hogwash.  They may compete among themselves but at the end of the day they and their teachers expect that they'll walk to the front of the line - right past the 'rest'.
So, not a fan of your little Honors programs. Honors programs need to understand that they showcase some of the best students NOT all of the best students.  Their hubris pisses me off to no end. If you'll note that it is implied by all Honors fans that the best of the best ARE there and if you're not then you're one of the 'rest'.  That's not elitist? Until they understand that they're just some of the best or even many of the best, then I think the undermine their own core value of meritocracy.

I'm very sorry for this. That said, I suspect your son's experience was unusual. At least it would not have happened in our department, where we eagerly celebrate and support our strong students whether they are enrolled in the Honors program or not.

Also, let me add (and I think that this is relatively typical) that our Honors program is not administered by our department. There is a university-wide Honors program, and our department's relationship to it is that they give us money. We can use this to run extra courses with small enrollments which would not happen otherwise. The catch is that the Honors College is looking out for their students and imposes hurdles for other students who want to take these courses. Sometimes we can get around these hurdles on behalf of our best students, and sometimes we can't.

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What are the goals and benefits of doing a PhD?
I'm a master computer science student in a German university and I will be graduating soon. I'm in a situation between accepting a PhD position or leaving academia to start looking for job. This is a very hard decision to make so I need some advice.
I see most of the people who do a PhD leave academia afterwards and start looking for jobs (is it also the same in the US?). Very few people continue with a postdoc and remain in academia after getting the PhD.
My question is then, what is the point of doing a PhD (especially if one gets a job in industry afterwards)? What are the benefits of spending 3-5 years obtaining a PhD? What kind of goals should a person enrolling in a PhD program have?
From the point of view of industry, I realize that after a PhD they might start with a high position in the company. But, on the other hand, in those 5 years they could have started a small tech company and make it somehow medium or even a bit successful. Instead of doing a PhD, after 5 years of investing in their own company, they could be paid for working for themselves and not for others, having their own companies.
From the point of view of obtaining knowledge, if someone is curious about knowing, they could learn new things by themselves. After graduation, finding a job or starting a company, knowledge could be obtained by buying books and reading during one's free time, or following extra courses. I don't think you don't need a university for this.
Am I right in my analysis? Is it true most people go to the industry after the PhD (I'm especially curious about people in the US from top universities)?
If my analysis is at least partially right, and since there is other viable ways to become successful in industry and to obtain knowledge, what are the benefits of doing a PhD? Is it only a good idea for people with strong plans to continue in academia, or are there other goals one can achieve (better) by obtaining a PhD? I am afraid that doing a PhD might be a waste of time if I plan to continue in industry.

This is pretty subjective.  It depends what you consider a waste of time.  Do you actually want to ask the concrete, answerable question 'Do most people who do a PhD leave academia afterwards?' or the more subjective question you are asking?  I don't think most people I know who completed their PhD and then left academia would consider the time spent doing their PhD wasted, thought certainly from a purely financial point of view it probably was.

Honestly, it sounds like you've already made up your mind.

@JeffE I would be really thankful if you can give me some opinion. Like the one from Peter. I'm interested in hearing what you think.

@TaraB I agree, from a knowledge point of view it was totally worth it. But my argument was that a person could potentially just study at home through out the years to gain knowledge if he or she is not interested in continuing for the academia afterwards.

@AlexTwain: Not just from a 'knowledge' point of view but the whole experience.

Is climbing a mountain a waste of time?  For most people, yes, of course.  But for a few, it's the opposite; the mountain is part of them, and they have no choice but to climb it.  Getting a PhD (and more generally, doing research) is the same.

Well, after graduating you face some thirty-something years of work. You have some choice on how to spend them. A minor quibble: Gaining knowledge is not the same as doing research.

Isn't doing a PhD a waste of time for most who did it? Definitely No!

I tried making the question a bit more objective. I still left all the arguments, but I tried to focus on the benefits of obtaining a PhD, especially if one is not continuing in academia. I think this can be answered more objectively, and still answers the OPs dilemma.

I'm late on this but wanted to comment. I'd first figure out where you want to go and align to that. Depending on what you want to do and where you want to go the PhD may or may not be helpful. Career counselors can help give advice here. Cross check what they say with employers where you’re looking to go. HR departments are usually helpful here in terms of giving honest input in terms of what they are looking for in the jobs you’d be looking to get.

You state that:

Of course they might get a high position in the company, but in those 5 years they could have started a small tech company and make it somehow medium or even a bit successful. After 5 years with doing that, they are being paid by working for themselves not for others and having their own companies.

The big obstacle here is that people need to have a strategy and an idea in order to found a start-up. If you don't have the "next big idea," what are you going to do to convince outside investors and customers to do their business with you instead of someone else? The challenge is that many people finish their bachelor's or master's degrees and still don't really have a strong sense of what they want to do, in part because they don't know what their options are.
Moreover, in many fields, what kind of company can people found? What kind of company would a chemist or economist going to found after undergraduate training? In many fields, training at the PhD level is often needed in order to develop the ideas needed for bigger ideas to take root.
Now, this isn't universally true—perhaps you have found what your big idea will be through experiences at an internship or in a bachelor's or master's thesis. If that's what motivates you, great.
However, you also equate leaving academia as "failure." There are many people who do a PhD—including some of my own students—who do not want careers in academia; however, they want the extra training to broaden their horizons and prepare themselves for a career in research and development in industry. For them, it's not a failure if they don't choose academia as a career, it's them achieving their desired objective!
The only way the PhD is a waste of time is if recipients choose to pursue a career that does not take any advantage of what they did as a PhD student, and those are relatively few and far between (at least in fields that what we consider "professions" instead of "jobs"). The reason for this is that a PhD (at least in the sciences) recognizes the ability to learn how to solve problems in an original and independent manner. In the humanities, a PhD tends to represent the ability to synthesize and analyze information in a meaningful way. The specific thesis project is the vehicle for expressing this ability, rather than the exclusive "goal" of doing the PhD.

standard disclaimer: my experience is with computer science, and in general I have familiarity with STEM, but I know almost nothing about Ph.D training and skills acquired in other areas
There are a number of misconceptions implicit in your question that other answers have picked up on, but that I thought I'd distill out here:

Very few people continue with a postdoc and remain in academia after
  getting the PhD. My argument is that wasn't the PhD just a waste of
  time for them? I mean they spent 5 years on it and then they left to
  look for a job in the industry.

The assumption here is that the topic you do research on is the main consequence of doing a Ph.D. In a literal sense that is true: your dissertation is on a particular topic. But as @aeismail points out, the dissertation (and a Ph.D) is a vehicle for training you in a certain way of thinking: analytical, critical, and inventive. These skills are what get you hired at jobs 'outside academia', and it's fair to say that without the training you get during a Ph.D, you will find these skills difficult to acquire (I'll never say it's impossible).
In that respect, it's not a waste at all. You spend some number years learning how to approach ill-structured, ill-defined problems, break them down, and figure out ways to solve them by yourself with no direction. This is a very valuable job skill that employers love to have.

Of course they might get a high position in the company, but in those
  5 years they could have started a small tech company and make it
  somehow medium or even a bit successful. After 5 years with doing
  that, they are being paid by working for themselves not for others and
  having their own companies

As others have pointed out, starting a company requires a different set of skills. In the tech world, having tech skills definitely helps to run a company, but there are thousands, if not millions, of people with the requisite tech skills, and very few of them become successful entrepreneurs. So it's not enough just to have some technical knowledge, and so it's not the case that you can swap out X years of a Ph.D with X years of working and expect to achieve some degree of success. Again, not impossible but certainly not guaranteed.

My other idea is that if someone is curious about knowing and getting
  knowledge. I mean you could definitely graduate, find a job or start a
  company and buy books and read all night or weekends! You don't need a
  university for this.

You don't need a Ph.D for this either. If you think that a Ph.D involves learning and reading, you're very mistaken. A Ph.D involves doing. You learn to reach the cutting edge so that you can do something new and creative yourself. Reading and reading will not get you a Ph.D - it might not even get you a single creative work !
p.s I've worked both in industry and (now) academia after doing a Ph.D from the US.

I would say, for people who enter a PhD program with defined and established goals, and with at least some understanding of what they are getting into, obtaining a PhD is almost never a waste of their time. Some great advice on what is good to know before dabbling in research, take a look here.
The thing is, a primary goal of a PhD is not to obtain knowledge. I also know that from the industry point of view, it is sometimes viewed as equal to X years of work experience, but that's not completely correct either: a PhD is about learning how to do research independently. While it is possible to get those skills alone, (usually by a lengthy trial-and-error process), the best way is under supervision and with advice of an experienced researcher: a thesis adviser/supervisor.
A PhD is kind of a stepping stone for academia: you don't have to continue if you don't want to. If you have an aptitude for research, it is an valid option to explore. Research, while closely related to academia, is not only performed in academia. It is a time to taste research and academic life. If it is something that you are interested in, even trying and deciding you don't really enjoy it is not a waste.
Finally, after obtaining a PhD, if you decide to leave academia, you will be qualified for different types of jobs in industry than somebody with just a Master degree. Somebody with a lot of knowledge might know which known approach to apply to solve a well defined problem. On the other hand, when developing a new application/product, it will be the job of an researcher to think of a best approach to a loosely defined goal.
Actually, as a personal side-note, when I just started my PhD my supervisors asked me if I wanted to continue in academia or go to industry afterwards. They said they could help me shape my CV and research activity so it's better suited for my choice: I told them I had no idea and had to see for myself for a while longer. A year after, I told them that unless something drastically changes, I want to stay in academia, but I'm sure they would equally accept me wanting to go to industry.
And lastly, to comment on your "starting a small company"... doing a PhD, investing in a career in a company, or trying to start your own company are, in my opinion, all "business ventures" of the same type, and equally valid or equally a waste: if you do something you don't have an aptitude for and what you don't have motivation for, it's a waste of time. Doing a PhD is as valid for a career beginning as any other job. It's just that not everybody wants the same career.

I'd like to second the notion that "you will be qualified for different types of jobs in industry".  A PhD doesn't teach you how to be a code monkey, as many of the PhD students I've worked with have found out when employed as, erm, code monkeys.  It teaches you other, deeper, computer science and research skills that can be applied to more specialised software/industry roles.  Usually roles that are more fulfilling tbh.

I believe the problem lies in that you view a job outside of academia as a failure, it is not. There are jobs that require a PhD in industry and elsewhere outside academia as well. What is a failure is foremost a question of the personal goals of the person in question. Industry and academia compete for the graduates to a large degree. It is obvious that how severe this competition is, depends on the subject but in technical areas it is definitely the case. In my own department it is very clear that people who finish a PhD end up in very good jobs. This, despite the fact that it is not a world were industry jobs are plenty, instead it is consulting businesses and government positions that are the norm.
There is not room for every PhD in academia. Not everyone is interested in an academic career nor suited. In general a person with a Phd has deep understanding and skills to solve problems, disseminate results and communicate these to others. There are thus many positions that require such insights to take on positions of responsibility in organizations, be it private or public.

When you start a PHD, you are not sure if actually doing the research required for getting that PHD, will be fun enough (you do not do it for the money anyway). After finishing it (for those who do) then you know if you really like to be in academia or not. Previous answers (mainly of user14449) already highlighted the problems associated with academia, which are only visible from INSIDE academia.
Also a PHD does not neccessarily has to be another step in your ladder of "success". There are many who are doing a PHD because a) they WANT to do it b) they know it in their hearts that they CAN do it. Even if they "waste" 5 years of their lives (as you put it) they want to do it, regardless if they get a job in academia, get a better job or become rich. It is like playing with a rock band. If you do it for becoming a rock star you will never become one. If you like music, you might actually have a chance.
On the other hand, only MSc students have the misconception that if they are going to create a new start-up company, they will become the new Steve Jobs and be rich beyond belief. The truth is that 99% of the start-ups actually fail (once external funding is spent) and only 1% survive. You say you are from Germany. How many CS start-ups are from Germany? Even there, most successful industries cooperate with reseach institutions like Fraunhofer or DLR which a) are connected to academia b) having a PHD certainly helps you to get a job there.
So the real question is: What do you really WANT to do? If you like to do research regardless of money, go for the PHD. If not, go to industry. If in doubt, stick with industry.

I'm not from the US, let alone from a US elite University. However, once I faced the same question. It's a decision you have to make yourself. Some notes:

When choosing between an industry job or a PhD, there is no wrong decision.
Other matters in life are way more important.
I chose the industry and I'm happy with my life.
I saw top-notch stock trading jobs passing by because I have no PhD. You just don't notice right now.
I see peers failing their PhDs.
It's about what you want to do the next years, not after that.

EDIT in response to your question:
From childhood on we've invested in our futures. By going for higher education, we thought in the long term. At some point we'll need to reap the rewards. Nobody ever wished he had worked more in his life when he was dying. Working should be a means (imho), not a goal. So to continue following a working strategy for life, you'll need to value the SHORT term more as you get older. Otherwise you risk never being happy with what you have and always working for something that will never come. Slowly switching from long term thinking to short term thinking may start by looking at a 5-year timespan. You don't want to be unhappy for the next 5 years in order to hopefully have a better life after that. If you can be happy with less money and more interesting work, THAT should be the reason to go for a PhD.

Can you explain further the second and last points?

I like what you said

There are a number of subjective terms in your question so answering the overarching question if pursuing a Ph.d is a waste of time creates a few questions within itself, however, a few points:
I'm in a situation between accepting a PhD position or leave the academia and start looking for job.
If the position in question pays the bills and allows you to gain work experience (assuming that you do not have any), then accepting a position for a year or two and then going out into the corporate realm may make sense.
I mean they spent 5 years on it and then they left to look for a job in the industry.
In the US, university professors with tenure or on the tenure track tend to see the better rates of pay and benefits -of course there are a number of caveats since some schools can be considered more elite than others and location is a factor. There are companies such as Google and IBM that pay Ph.d graduates very well to solve real world problems and to further their business objectives.
in those 5 years they could have started a small tech company and make it somehow medium or even a bit successful.
Running your own business usually requires a lot of time and effort -if you wish to be successful anyway. So folks may not wish to put in that type of commitment especially after surviving 5 years of Ph.d work, a relaxing 30 - 40 hour work week with paid time off and benefits could look appealing especially if there is a family with children involved or caring for an aging parent.
My other idea is that if someone is curious about knowing and getting knowledge.
This depends on if there is a genuine interest in research. If one wishes to see the fruits of their labor see the light of day in a commercial sense,then going to the private sector may allows one to see their research come to life and touch the masses. Another commenter made mention of potential issues with jealous colleagues, people that try to steal your work, etc -these elements also apply in the corporate world especially if there is some sort of compensation at stake (it is not always financial by the way) so each avenue (academia vs. corporate) has its on rewards and pitfalls.
So, I suppose it comes down to your original motivation for school. Was the plan to work in academia, private industry or a combination of the two? Either way you go, you will gain a life experience that you did not possess before so, its comes down to how you wish to make it work for yourself.

Your question reminded me of the blog post linked below.  See what you make of it!
Generally speaking, existential decisions that are based on binary alternatives can easily be wrong, since there are usually many more alternative pathways in reality.  Thinking in terms of binary options is just not the best way of coping with life, I think, if you excuse my binary assertion... ;-)
http://alexandreafonso.wordpress.com/2013/11/21/how-academia-resembles-a-drug-gang/


text:
Can I get a faculty job in the UK without UK experience?
I have worked as an Assistant Professor in Japan for 5 years and can apply for promotion, but for personal reasons, I cannot live in Japan. I plan to apply for a Senior Lecturer/Reader position in the UK.
A friend of mine who works in the UK told me you cannot get a teaching position in the UK unless you have studied or worked in the UK higher education.
She suggested that I have a better chance to get a job in the US where universities do not expect a local experience if the application is strong at the international standard.

This is not true, I can give you countless counterexamples from my narrow fields. Many people becomes lecturer (i.e. assistant professor) after PhD/postdoc in Japan/Korea.

Could you clarify whether your friend meant "cannot" in the practical or theoretical sense?

I am not sure what type of answer you are looking for. Based on personal experience as an American with all my education and training in the US, my first faculty position was as a lecturer in the UK. There are no laws requiring UK experience to get a faculty position of any rank in the UK. There are laws that give preference to those who have a right to work in the UK, but that is not the same as UK based teaching/education experience.
While some schools may prefer individuals with UK based experience, it was never something that came up during our searches. That said a familiarity with the UK system is helpful for demonstrating you can be a good tutor and help advise students.

The US and UK systems are similar. I think the point mentioned in the question is that UK universities do not trust someone who has successfully worked in Japan (I personally have no idea how is the education system there) can meet the teaching standards and norms in the UK.

@All apart from being taught in English, I wouldn't describe the US and UK systems as being similar. That said, if the question is really is Japanese experience valuable when applying for a UK job, the OP should edit the question.

Then, as an American working in the UK, you have perfectly answered the question: your chance is the same in the UK and the US.

@All and we hired people from Australia, Germany, France, Netherlands, Canada with no experience with the UK system. I don't recall ever seeing an applicant from Japan, but I don't think it would have mattered.

Definitely hiring from EU countries is much easier than from North America, because EU has a harmonized education system with lots of exchange programs such as Erasmus. As you mentioned, some universities prefer not to sponsor for the work permit. In this case, I think Australians and New Zealanders can get the work permit easier.

In addition, EU law requires third country applications only to be taken when there is no suitable EU candidate (of course there are many ways this can be gamed if desired - in particular with very narrow or tailored job descriptions).


text:
How does a highschool student intern under a professor?
I have read that interning under a professor can not only help you gain a better understanding of a subject but also it can look good on your college resume. I was wondering how I could possibly do this in ninth grade. Do I email the professor I want to research under or does he have to ask me or can it be both?

Where are you in the world?

What do you expect the professor to gain from this? Supervising someone can take significant time, which professors are short of, and in many fields even a late undergraduate may not be able to provide any meaningful contribution to research.

You may want to look into maths, physics and chemistry Olympiads, who is in charge of organizing them nearby you. These are events for high school students which provide links to universities. When I attended the national Spanish Olympiad there were a few participants that had been training with college professors. This would open up the possibility of doing research to you. It goes without saying that you must be really smart for a professor to be interested in mentoring you at this stage.

Your goals are laudable and do not be discouraged by naysayers who say high schoolers should not get research experience. I had research experience in high school working with biologists at an army base and National Wildlife Refuge when I was in high school.
Now, to answer your question. The short answer is do legwork and research nearby universities. Here are examples I know about:

Some universities have formal outreach programs for high school students such as this archaeologist program.
Some professor will take high school students as interns. For example, my advisor lists his high school interns on his CV. Note that CV is basically an academic resume.

Here are suggestions for finding these opportunities:

Try to find a "mentor" who is doing research. Ask them for an informational interview. This could be someone who works as a scientist or maybe one of our high school science teachers. You probably know someone who knows a scientist even if your personally do not. Ask your parents, high school teachers, family friends, scout leaders, people from church, etc. if they know anyone. Basically, tell them "I think I want to be a scientist. Do you know anyone who is one
that I could ask about their job?" Do not hound this person about their job or expect to get an internship with them. Instead, ask them how they would get an internship if they were in your shoes.
Browse and search homepages of universities and their academic departments and faculty. This will let you see what type of research exists at the school and might help
Look at the "Continuing education" or "public outreach" or similar programs such as Upward Bound.
Expand your search beyond universities. Look for internships at nearby industries or government facilities (e.g., government labs, state parks, wildlife reservoirs, fisheries centers, etc). All of these places employ scientists including chemists, geneticists, biologists, ecologists, and more.

Note in case you live in a rural area: Even if you are in a rural area or small town, people do research. You county likely has an extension agent (For example, Wisconsin has UW-Extension and your state if in the US likely has one too). Some people wrongly think of farmers as backwards people, but they are wrong. Modern farming uses lots of science. In addition to extension, look to ag for other scientific applications such as genetics and self driving cars. These companies have representation in rural areas. Even if you do not want to study these fields, seeing what they do would still help you to better understand research.

In the field of life sciences, I've seen five methods:
1. Research programs for high school students
Most research programs are for undergraduates, but there are occasional listings for research programs for high school students. Examples in Canada include:

The Samuel Lunenfeld Research Institute SciHigh summer research internship. It's for Grade 11 and 12 students, and it's based on a 500-word essay, two references, and a resume.
The Gene Researcher for a Week program by the CIHR's (Canadian Institutes of Health Research) Institute of Genetics. It's a week-long internship over March Break that teaches you either wet lab or dry lab techniques. You must be 16 years or older.
The Hamilton Health Sciences Summer Bursary. It's a 7-week summer internship for Grade 11 and 12 students in Hamilton, Ontario.
Sunnybrook Hospital's Focused Ultrasound High School Summer Research Program. You must be 16 years or older.

2. Science competitions
You can either participate in a competition that place you in a laboratory, or win a competition to earn a laboratory position (either as a direct prize, or to strengthen your applications to future research positions). Examples in Canada include:

The Sanofi Biogenius Competition. You apply to enter a competition, and the organization connects you with a lab to manifest your research proposal.
The Canadian Brain Bee. It's a written neuroscience competition, and the national champion wins a research placement at a neuroscience lab.

3. Cold emailing
This was my path. Below is a plan based on what worked for me:

Develop a theoretical background to the level of a first-year undergrad. The most popular intro book in biology is called Campbell Biology.
Find a list of labs you wish to apply to. Go to the websites of local universities, and create a short list of professors whose work interests you.
Read the description of each professor's research, then read their recent publications (often listed on their website). You can look copies of their papers on a website called PubMed.
At the same time, train yourself in wet and dry lab techniques. Familiarity with Excel is a must. You can try to train yourself in wet lab techniques at your high school (I entered a biology competition and trained myself in lab techniques after school), and learn software at home.
Email the professors. Be courteous, keep each email relatively short, and don't expect a response. You'll likely have to email a large number before you get a reply. If you actually familiarize yourself with their research, this should take a long time before you earn an acceptance (if at all). Don't spam a copy-pasted email.

4. Connections
If your parent or relative is a researcher (or knows someone who is), you can ask them. Many high school interns work in the lab of a parent or relative.

The bottom line
If you're interested in becoming a scientist, research experience is a great way to see if the field is right for you. To become a strong applicant for a research position, you'll need high grades, strong reference letters, and an advanced theoretical background. You can earn these by studying efficiently in school, and getting involved in extracurriculars.
But above all, take some time to enjoy high school. Go on dates, explore your interests in areas irrelevant to research or career, and spend time with your friends. It helps prevent burnout, and the most productive life sciences researchers in the world balance their time, even those who lack genius-level IQ.
Best of luck with whatever path you wish to travel.

As enthusiastic as I'm sure you are about working in a research lab, it really wouldn't be in the best interests of any academic to bring a high school student into their lab.
Undergraduate degrees in the sciences, as much as anything else, teach students how to behave appropriately in a lab setting as well as chemical handling et cetera.
Working research labs are busy places with the work never being done for PhD students right up to the group leader, as such, I doubt that there would be many out there willing to take on such a big commitment.
I think, for now, the best you can do is to keep working hard at school, ask the lab technicians at your school if you can help out and see if you can build up some lab experience that way but maybe wait till you get to university for the research labs.

Good answer. Just one small point to add: Some colleges offer visits to highschool students, like "get to know the university/the lab/etc." These can range from a short guided tour up to a whole week being introduced to the beauty of the field, and might be a good chance for an interested highschool student to get a first impression and maybe even increase chanced to get into this college later.

Not all labs are this complicated. CS labs, in general, don't really have any technical skills as pre-requisite... I don't disagree with your general conclusion, but we have no idea the location or the field, it might be doable.

That's a very fair point, my background means I automatically always assume science when I see lab but you're right.

When I was in grad school, 2 or 3 professors regularly had high school students as interns in their toxicology wet labs. The students functioned as well as undergrads at doing lab work.

The OP didn't specifically mention research labs. There is a lot of research not done in labs. My own field of mathematics is an example!


text:
Analysing papers and providing search
Suppose I want to provide "smart" (AI, meaning extraction etc.) search over many published papers (specifically, biological) to simplify researchers' live.
Now, I have access to my university library that contains text of many papers from different sources, including those with payed subscription.
Is it legal to download all papers, analyse them and provide search without disclosing full text of the paper, only small part of text or image and with proper citation?

At a minimum it is probably against your library's terms of use of their resources, and it probably violates intellectual property restrictions to do it on that scale without permission. For example, for Google to be able to search a journal for indexing on Google Scholar, the journal has to give Google permission (though it typically goes the other way: journals are approaching Google asking them to index).

Bulk automated downloading is a great way to violate terms and conditions of access for most legitimate resources...

I do not see any problems with it as long as you disclose your methodical approach and as long as your university library's terms allow such a behaviour (which is doubted by Bryan Krause in the comments). Perhaps it is best to ask your university library just to make sure.
If the concerns hold, you could alternatively use open datasets of full-text scholarly publications. Just to name three examples:

The Semantic Scholar Open Research Corpus (S2ORC), comprising 12.7M+ full text papers from various disciplines.

The Elsevier OA CC-BY Corpus, another cross-disciplinary dataset that entails 40k full-text papers.

CORD-19: The Covid-19 Open Research Dataset.

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


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Is it okay to take a day off as an undergraduate?
I am an undergraduate Computer Science student. I take the bus to college everyday at 7 am and come back at 4 pm. And take 3 lectures everyday, except on one day, I take 4, which are 1:30 hours long. Due to this I get very tired, especially towards the end of the week. Anybody would.
I have Saturday and Sunday free. I was thinking whether I should take the Saturday off, or should I study that day too just because I feel like there is a lot to learn. Also sometimes I have my own projects to work on and I have to take a break from the Course's material on weekends. Is it acceptable/expected? Assume I can complete all my assignments in weekdays and on Sunday.

That depends entirely on your goals and your capacity to learn effectively without taking longer breaks. I don't think I would want to learn six days a week, and I don't think I could either. But people are different.

How would anyone know to disapprove?

Your health is important to maintain. It does you little good to work harder than your mind and body can accommodate.
Burn out is a serious issue. Some people work so hard for so long that they just, one day, decide it isn't fun anymore and quit, cold.
Your mind will continue to work on problems without being conscious of it and without being forced to concentrate on those problems. People often wake up in the morning or after a nap with a solution to a tricky problem.
So, yes, learn to take breaks, whether short or longer - preferably both. Work when you are relaxed if you can make that happen.
You can also, perhaps learn to use some of the travel time to either just relax or to work on things that don't require access to a machine. This might make the "day off" less of an issue. But don't take this suggestion to mean "work always". For example, some people carry index cards on which they write definitions of things or something about a current problem. If they find a moment of boredom, say on a bus, then they can pull out a few cards and leaf through them, just reinforcing their learning.
See Hipster PDA, for example.

Of course it's OK.  Even leaving aside the psychic issues of what is your life for (is it to work or to enjoy), there is the concern that your efficiency drops if you are too tired.  Several studies have been done showing that students who burn too many hours may get better grades if they spend less time. It's not a general thing and there are many who need to do more.  But it is not uncommon either.
Actually my bigger concern is your efficiency and rest state DURING THE WEEK.  You mentioned getting tired as the week goes on.  A day off isn't probably the best way to recharge this.  You need to keep strength up during the week.  Try to think of how to use your time more efficiently (an easy one is to wolf lunch in 2 minutes and then use lunch for exercise or study).
You also need to think how to use the bus rides best.  I think notecard drill is a GREAT suggestion.  It's active enough (versus reading) that you won't get sleepy.  But doesn't require huge concentration or a great writing surface.  When I was younger, I could get regenerative sleep on the bus but as I age, I find this less good--have had jobs several times with 1 hour+ bus rides (one way).  Don't know for you though.  Maybe sleep one leg and drill the other?  In any case, this is a problem to figure out.  Even living on campus (or walking distance) might be an idea.  I understand if money is the issue but if you are far away to be with buddies, I would ditch that.  Commutes are a huge waste of time in the universe.
P.s.  As far as the notecards, we didn't call it "hipster", but it was a common advice in the military to have a few note cards with you.  You can take notes or write ideas.  Can drill things (e.g. casualty immediate actions).  The other thing is there is a STRESS REDUCTION aspect to having the cards.  If you are trapped in a line at the provost, grocers, etc. instead of being POed and stewing, you pull out the cards to drill.  Leaving aside the benefit of the drill (and there really is some), you have the stress reduction at not feeling trapped and angry at the time wastage.

Wolfing lunch in two minutes is not good for health...

It is if you use the rest of lunch for a workout.

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


text:
What options does an international PhD student in UK have to fund his PhD?
I am in the final year of my PhD and have some dues to clear. Unfortunately, I don't have enough funds to pay my fees. What options do I have, being an international student, to obtain financial assistance to finish my degree?

Advertise yourself as a private tutor in your subject. As a PhD student you have a lot of expertise and could easily tutor GCSE, A Level or even undergraduate students. The going rate for such tutors can be as high as £20 p/h.

@astronat £20 per hour of contact time. An hour with a student can often require an hour of preparation, especially if it's the first time you've taught the particular course.

This is something your advisor and your department should be advising you about. It's literally their job to know about these things. Sources of funding are usually at least somewhat subject-specific but, even if you told us what you're studying, we don't take this kind of question.

Do TA. The easiest way is to do TA for the courses that your advisor or professors in your group teach. I was paid £12.XX per hour at my school in London. As long as it is less than personal allowance (£7000 per year), you don't have to pay tax or anything, and it can be added on top of your scholarship, so it's good.
Find an internship. My scholarship prohibited me from taking internship so I was kind of happy when it expired.
If you major is CS, there is some programs like Google Summer of Code (open in February), which you can earn > $5000 for 3 months with no tax.

The standard tax free personal allowance in the UK is currently £11,500.


text:
How to manage an interview by videoconference?
I am working in academia in a position that is similar to instructor. The job is great but I am working under a short-term contract system with last-minute renewal notice, so I am trying to move for a more stable position.
Since the positions I am looking for are mostly in other countries, my interviews are held by video-conference. Some allow Skype interviews, but others ask for a "professional" video-conference, with high-quality video, and good and stable internet connections. Basically, they want me to use the video-conference room in my current institution.
I was wondering how people usually manage their organization for this kind of interviews. My question is 2-fold:
Questions

How do institutions feel about letting their employees using their video-conference resources for job prospecting?
How do researchers that are not currently working for an institution find the resources to participate in this kind of interview? High-quality webcams are expensive.

"but others ask for a "professional" video-conference, with high-quality video" Really? All remote interviews I have ever seen (including interviews by Google, Microsoft, and IBM) were typically done via telephone or Skype. It indeed seems weird that they assume video conferencing to be available - not even my research group has such equipment, and I wouldn't know what we would use it for if we had it.

Since I do much of my work by video link, I have some experience with the problems of conducting business over video-conference.
For permission, in universities it will generally be fine as long as you aren't disrupting the work of others.  If there is any rule regulating video, you should be aware of it (e.g., some non-university research institutions don't allow video-conference at all, and make very certain their researchers know).
For quality, I would guess that their actual requirement is not HD, but that they want to be able to read your expression as you talk. Here, the primary limitation is not your camera, but your network connection. The built-in camera for your computer or any cheap webcam will generally produce much higher quality video than you can transmit effectively.  Things to do to ensure a good connection:

Use a wired link (e.g., EtherNet) rather than wireless if possible, as your connection is likely to be better and more stable.
Use headphones and a microphone (cheap earbuds with a built-in mike will do): the headphones will prevent echo from your speakers, and the microphone ensures consistent pickup of your voice.
Different software provides different quality tradeoffs optimal for different connections:

Professional videoconferencing hardware (e.g., PolyCom), is nice if your institution has a room and you can get help using it.  Its learning curve is a pain, and it's not any better quality than...
High-end videoconferencing software (I've had good experience with BlueJeans), provides a fantastic quality connection but has brutal demands for bandwidth and processor power.  If I use it for more than ~2 hours on my laptop, it overheats.  Note that you don't have to buy this software: generally, only the meeting organizer needs to, and you can connect via a web link that they send you.
Skype is good for mid-grade connections: it provides nice video when given a consistently good link, but degrades badly if the link is inconsistent.
Google Hangouts is good for low-grace connections: its video quality is never particularly good, but it will get something through.

The most important thing is the high-bandwidth link: with a good enough link, Skype is generally sufficient within a continent.  For very long distance connections (where the limitation is lag and undersea cables) you may want to use higher grade software. If you can't get access to a place that gives a strong connection, arrange the connection for a time when you are likely to have little competition with others for bandwidth.  Early morning is generally best: during the day work activities consume bandwidth, and in the evening people are watching video.

Good lighting is also important. It can be difficult to get a good image if you're being backlit by a window. Bright lighting is good as it allows the small cameras to get a clearer image, but if you're near a window try to be lit from the front or side.

@Moriarty Good point... cameras have much worse dynamic range than our eyes, and are often pretty stupid about how they use it.

Regarding institutions, I have gone through the regulations in mine (the Swedish equivalent of a national laboratory), and they don't specify any usage limitations. This makes sense, after all, most of the time they sit unused, and you don't wear them out by making a call. I would assume that if someone makes such a heavy use of it that it is disruptive to others, will be asked by the administration to explain it. But a few interviews will not by all means be so.
YMMV, but if the regulations don't forbid it, you are probably fine.
Regarding the second one, an anecdote: the only online interview I had for PhD positions was done audio only over Skype. The professor didn't have a working video set.
An institution demanding to interview you over HD video sounds suspicious.

However, if you don't want to reveal to your current institution that you are interviewing for other jobs, it could get sticky if they want to know why you want it, or if someone walks in during your interview.

@NateEldredge I don't think anyone reasonable would object to the OP looking for a better position given that he is in such a precarious situation; but I can imagine people who would.


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How should one react when one's work is rightfully critiqued during a conference presentation?
When somebody presents the paper, the attendees ask questions about the paper. But what if they raise a legitimate objection when they ask about our work and we know that they are right? Should we accept that or should we defend ourselves?
I ask this, because recently I attended a conference, and in one presentation I saw an important mistake on one of the presentations' algorithms. But he denied my reasons, and both of us knew that my reasons were legitimate.

How can a question be wrong or right?

@dgraziotin :  escaping from a possible question that highlights an issue in your algorith

@ORBOTInc. :  escaping from a possible question that highlights an issue in your algorith

@dgraziotin So what is the meaning of defend

Defend means to be prepared with an argument. In other words you know what you know. But that doesn't mean you know everything about the topic. In a practical sense, dialog, clarify and make an effort to learn something new from the question. The purpose of academia is to share ideas and insights for the betterment of the field that you're in. It is not to better your position. That is only done through your contributions. Read up on critical thinking in philosophy for what a defense may mean.

Should we accept that

Yes.
If somebody points out a flaw in your work, be thankful. They are giving you free advice. Don't try to be right at all costs. Of course it's awkward when people point out major flaws in your work when there is an audience, but it's part of the game.
If you believe you are right, defend your point using objective arguments. If you know the critique is founded, accept it and try to make the best of it.

I've been on both sides of the podium for this sort of situation, and there are a number of issues that make it not straight-forward to deal with.  Most importantly:

The questioner may misunderstand the material, either because it was presented poorly or just because it's hard to wrap your head around new material in the middle of a talk.
There are often subtleties that mean the presenter may not be able to analyze a new potential flaw correctly in the moment.

If you are the speaker, then you need to be open to the fact that you are wrong: don't get defensive about your work.  At the end of the day, it's not about you: the world is what the world is, and no amount of defending your position will change the facts.  If you agree with the questioner about the flaw, then you need to admit it.  This has most frequently happened to me when I am giving a class lecture and a student notices a potential mistake on a slide: rather than look at it as a problem, I thank the student and turn sanity checking the equation or algorithm into part of the lesson, where we exercise other knowledge and intuition to check the material.  That's generally less possible in a conference talk, of course.
If you disagree or aren't sure that you agree with the questioner, though, don't get into a fight.  If you can show they are wrong simply, do so simply and gently, with the assumption that it is a misunderstanding (per first bullet above).  If it's complicated or you aren't sure, just say so and offer to talk with them about it more outside of the talk.
Conversely, if you are the questioner, you don't need to make the other person admit defeat.  Even if you are right and the other person is confident enough that they would be willing to admit it, they may not be in a position to do so because they've only had 30 seconds to consider it and aren't certain enough whether they agree with your critique.  And if the speaker is not self-confident, they may be too afraid of losing face to admit an error directly.  That doesn't matter: if you raise an issue publicly, such that the rest of the audience is not blindly accepting a dubious element of the work, that is enough.

So a third person could nail the problem of your algorithm just from your presentation, without looking at the code for hours!? You'd better not deny it completely, because there'd be others who thought the same, but were not really sure. You would look really dumb to all of them if you plainly denied it or brushed it away.
"We will look into it." and "We should discuss this over buffet." could be two possible answers, a good answer would combine the two.


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Modified picture based on three different sources - citations needed?
I am thinking about where the borderline is with citations.
I made a new picture based on three different sources, so I wrote under the picture "adapted from [3,6,9]." This, however, seems to be funny.
When do you need to include citations for your modifications of pictures?

I think your first instinct is correct, it just needs a little bit of clarification in wording.  I would suggest something like:

Created by combining adaptations of Figure X from [3], Figure Y from [6], and Figure Z from [9].

how would you do this in APA style? Using commas or semicolons?
Such as: (own illustration based on source A; source B; source C)

It depends on what kind of information you are adapting from original pictures.
If original picture has some very well accepted content in field which you are adapting, you can modify it and use it in your figure. In that case you don't need to give citations. For example, if you are using symbols used in original figures which are well accepted in field, you can use without citing original source.
In contrast, if picture has some new content or some unique concept which you are adapting then you should acknowledge it. For example, if original figure is showing some unique symbol which is output of their new research or imagination, then you should acknowledge it.
However it is always best practice to cite all images from which you have adapted content.

When do you need to include citations for your modifications of pictures?

ALWAYS.
Any time you modify somebody else's work, you must cite them.

Would the downvoter care to explain in what circumstances they feel that it's appropriate to modify somebody's work without citing them?


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Should I add the "presenter certificate" to the paper presented at a conference?
I have presented a paper at a conference and received a certificate proving that I was a presenter.  The conference does not have an English agenda, so it would not be easy for an application committee to find proof that I was the one who presented it online.  I am now submitting the paper as one of my writing samples for a Ph.D. application.  Should I attach the presenter certificate to the paper, in order to prove to the committee that I was really the one who presented it?

I'm afraid I don't understand what you're asking.  What is this proof of being a presenter?  What do you mean by "merge"?  What are you planning to do with the merged document?

The vast majority of conferences don't offer 'certificates' to presenters, and no reasonable institution will expect to see such a certificate (or any other 'proof' of presentation). (Same applies to this related question.)

Thank you all. I am applying to phd programs and I asked the society for the certificate of being a presenter; for they do not have an English agenda or post. So I think it would be necessary for me to provide a sort of proof, like I also provide the preprints of my accepted papers.

@ff524: Then would anybody can claim to have presented her papers at some conferences?

@ff524: And why we applicants have to clarify that the journals publishing our papers are not predatory to a certain degree? Isn't it because we want to prevent ourselves from being considered as one who bluffs? I think the same principle applies to claimed conference papers.

So, basically you are asking how to provide evidence that you were the one who delivered the presentation at the conference?

That is true, exactly

I have cleaned up this question and made it more focused, per the discussion in the commentary.  Since I think the discussion in the commentary clarified the question, I have nominated it to reopen: the premise is mistaken, but a valid question that received good answers.

As per the answer to your previous question, you are not required to spontaneously supply proof for everything in your CV, and it would look extremely unusual to attempt to do so in this case.
The fact that you could be asked to substantiate anything written in your CV, and the consequences of subsequently being caught in a lie, are considered enough of a deterrent to prevent people from lying about their credentials. The standard practice in academia is not to include "proof" of everything on a CV unless explicitly asked for proof of some kind.
So in answer to your question of whether you should merge the "certificate of being a presenter" into the paper presented at the conference as part of your PhD application: No, you should not. You should not submit such a "certificate" at all unless you are explicitly asked for it, and I have never heard of anyone being asked for such a thing.

Thanks. Since my homeland is relatively unknown to the whole world and the conference is an annual conference of a local society, I especially desire to prevent me from being considered dubious. Please understand my situation and my intention. I know clearly that I am not seeking for myself troubles.

If possible, please let me know if you are a reviewer of an admission committee, would you view the records of a person graduated from a locally well-known university in an unknown country more stringent than those who graduated from the ivy league?

@Kurt Certainly the presentation is viewed differently because it's a local conference in an unknown country - but differently in the sense that it carries less weight and won't help as much for admissions, not that they'll suspect you are lying about it. Supplying "proof" that they haven't asked for is not going to help your case in any way, and will just look strange.

Ah, thank you. Maybe cultural difference takes place. Few months ago I discussed with a professor in my department my CV and writing samples. He told me, "How will you view applicants from extremely unknown countries? You doubt them". That gave me an impression that maybe more advanced countries would view me as such. Seems to me I had been be wrong.

@Kurt "Doubt" as in "doubt that their experiences are meaningful by Western academic standards," possibly. "Doubt" as in "suspect them of lying on their CV," not likely (unless there are things on the CV that seem especially improbable).

One thing to keep in mind is that certificates from a conference are easy to fake: anyone can make a plausible-looking certificate on their own computer, and the admissions committee will have no idea what a real certificate would look like.  (And even if the admissions committee somehow knew what it should look like, an applicant could copy/modify someone else's certificate.)  This makes them almost completely useless for verification.  The certificates may satisfy bureaucratic requirements among those who use them, but in practice they won't actually prove anything.
I would recommend against including these certificates with your application.  It looks suspicious to me, like you're presenting it as stronger evidence than it actually is.  In particular, people might wonder whether you are trying to prevent a more detail investigation by preemptively offering a certificate.
However, this isn't a particularly important issue, since the admissions committee probably isn't worried about whether you actually presented the paper at this conference.  A conference presentation is not meaningful or worthwhile for its own sake, regardless of quality.  There are conference with low standards (where bad work is sometimes presented) or no standards at all (where anyone can present whatever they like).  Instead of being worried about whether you presented the paper, the admissions committee will instead wonder whether presenting the paper means anything.  That's much more subtle question, since the only way to convince them that the quality is high is if someone knows enough about the conference to judge its quality and is trusted by the committee.  In practice, the way this typically works is that if the committee really wants more information, they find a member of the department who has a contact in the country in question and ask them for their opinion of the conference.  (This can also lead to verifying attendance if necessary, since the contact will presumably have the appropriate language skills and can also get in touch with the organizing society.)

Thanks so much. Your suggestions, together with ff524's, are strong enough to convince me not to put the proof in my writing samples; for it would backfire. That prevents me from wasting time.


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How many papers should a Ph.D. student review for their professor per year?
My professor asks us on a frequent basis to review papers and get together, discuss their merit and come up with a review. This happens in bursts, where I may do 2 one week 2 another and then go for 3 weeks with none and then back to having 2 or so a week to look at. There is never more than a 2 week notice given before we must have these reviews in. I would say at a minimum I review 6 papers a semester, with 10 being the max.
So my question is how much time should a Ph.D. candidate student be putting toward reviewing a paper? Also how many papers a semester or year would you consider an average having to review as a Ph.D. student?
Now realize I understand that I need to be reading papers and the state of the art in my field but that is not what we are asked. I feel it is more involved to come up with a metric of determining originality and such with each paper for a review.

The question seems to leave ambiguous what the purpose of this reviewing is (or at any rate I wasn't able to figure it out).  Are you reviewing papers that have been submitted for publication or already published papers?  When you say "come up with a review", do you mean a written review?  What is the stated purpose of this activity?

We are reviewing unpublished papers for conference and journal publications.

There is no hard and fast rule here: some professors don't ask their students to help review at all, others pass all of their reviewing to their students.  I think the latter position is generally indefensible---the professor is being asked to review because of their expertise, not their ability to press-gang students into doing work for them.
In my own thinking, the driving principle should be the education of the student.  Every person who is aiming for a career in academia will be asked to review, and every person who authors papers should have a chance to experience the reviewing process from the other side as well.  To me, though, that calls for a few papers a year, not a paper every week.
From your description, I'm not quite sure how to judge the situation with your advisor.  At first reading, my thought is that your advisor is accepting more reviews than they can handle, and dealing with the situation by passing on the reviews to you and your fellow graduate students, which would be inappropriate.  If your advisor is actually spending a lot of time with the paper as well, and essentially co-reviewing with you, then perhaps they just have a very unusual perspective on how to learn about paper-writing and the state of the field.
I think it also depends a lot on the quality of papers you are getting asked to review: if you are being asked to read good papers sent to top journals, then it's more defensible, since you really are seeing the newest relevant literature before anybody else; if there's a lot of low-quality stuff to iffy venues, though, it's probably a waste of time for everybody involved.
Bottom line: you're being asked to do an unusually high amount of reviewing, and if it's interfering with your ability to pursue the rest of your program, then it would be reasonable to bring it up with your advisor and ask for a change.


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Course Requirements for Mathematics and Applied Mathematics Phd admission
I am a student from Sri Lanka, and I have just finished my degree. Because of the rules of my University ( My program was a direct intake for Mathematical Finance specialization, and despite this I have followed mathematics subjects the most) I was not allowed to take any abstract algebra courses. I have completed the other courses which Pure Mathematics Special students undertake such as in Analysis and have good results. I will be undertaking a reading course for Algebra with the senior lecturer at the University at whilst he said he will give a letter as evidence as possibly at best a letter from the faculty it won't be officially recognized in the transcript
So my main question is that would such a letter be recognized, even if it is signed by the dean of the faculty when apply for a phd? I hope I will be able to cover the usual algebra syllabus and maybe even more.

Hi, and welcome to Academia.SE! As written, this question is likely to be closed as "too broad" because it contains several different questions within it; accordingly, I am going to edit to truncate to what you identify as your "main question." I believe that you may find what answers we can give for your other questions elsewhere on the site.  If you disagree with my edits, please feel free to revert or modify.

I would also like to know if its possible what kind of undergraduate
  requirements does an Applied Maths program usually look into? Would I
  be correct in assuming that they won't be looking in to algebra that
  much?

Not having had an undergraduate course in abstract algebra wouldn't be much of problem for admission to the graduate program at my institution (which focuses on applied and industrial mathematics.)  Background in analysis, differential equations, modeling, probability, and numerical analysis is much more important.  Significant background (such as a minor) in some area of science or engineering is also helpful.

The part of the question that I've quoted in my answer was edited out of the current version of the question- the quoted material wasn't drawn from my imagination...

Seemingly the question and Brian Borchers' answer refer to "applied math" in a certain popular (if narrow) tradition, so probably Brian's answer answers the question appropriately.
However, if "applied math" is construed as "math that is applied", then it would certainly include abstract algebra and number theory, for cryptography and error-correcting coding. It would also include things toward design-of-experiments. Game theory? It really does appear that there is no simply-described subset of mathematics that is "applicable" while others aren't.
But/and then returning to the part of the question about certifying acquaintance with abstract algebra: a direct letter of recommendation commenting on a "reading course" could potentially be stronger than a mere grade-on-a-transcript, so I'd think it'd not be an obstacle. If anything, the evidence of taking initiative is a big plus, in itself, when I look at grad applications.

I agree very much with the point that Paul makes here about the difference between "Applied Mathematics" (what's commonly understood as the content of a graduate program called applied mathematics) and applied mathematics (actual applications of mathematics that might make involve a wide variety of mathematical topics in diverse application areas.)  Sadly "Applied Mathematics" has come to mean something very specific.


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Paid publication fee and now no contact from journal: what should I do?
My situation is the following: I submitted an article to a journal which appeared in Scimago, the article got accepted, and they charged a fee for publication costs. I have now paid this fee from personal money using PayPal.
The problem is that it has been nearly two weeks since I made the payment and I have not received any email about it. I have checked my account and the payment has been made, wrote an email to the editor in charge within a lapse of two days, and have received no answer at all.
I am pretty worried about this situation, but how can I deal with it? I have tried to call their contact number and also gotten no answer at all.  Should I continue sending emails to the other editors of this journal or just wait until they give me an answer? I would not like to sound like I am anxious, but I believe it is pretty bad that at least they do not give an answer if they receive the money or not.

Do you mean that you paid with your own money and not with university funds?

I've done some cleanup on the post; please feel free to revert any aspects that you feel damaged the original question.

Have to ask: is there any chance this is a predatory journal? Being listed in a ranking doesn't necessarily rule this out. Do they publish what you regard as good work? Do well known experts in your field publish there? Did your interactions with the journal give you confidence that their peer review process is thorough?

It is not a predatory journal, I have checked it; also the list of reviewers were well known in the field. The peer review also gives useful insight