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Can a non-enrolled/non-registered student use the instructor's intellectual property under fair use?
What is the transaction being made by paying tuition at most US colleges/universities? Are you paying for the time spent teaching, the price of education/intellectual property, or the diploma itself?
More specifically: Assuming it is not being repurposed for profit etc, is the IP covered under fair use? If so, could a person auditing a class simply for the sake of learning legally take classes without having to pay tuition?

Please ask one question per post.  Also, https://law.stackexchange.com/questions/7683/in-the-us-when-is-fair-use-a-defense-to-copyright-infringement

What do you mean by IP? If, say, an invention by the instructor, IANAL, but I am quite sure you do not get any rights to that, even if it is taught in class. By paying, you get the right to a certain proportion of your instructors time and teaching expertise, and the right to prove that you are good enough to get a degree.

There are often specific rules that faculty cannot allow individuals to attend class sessions without formally enrolling in the course (perhaps as an auditor) and paying tuition.  Furthermore, there are often rules that class materials must be made available through a Learning Management System that makes it impossible for non-students to access the material.

@BrianBorchers good point, thanks.

There are two kinds of universities in the US: public and private. The public institutions are tax supported, though not completely. The private universities see to their own funding. Public universities are governed by rules defined by the individual States with some regulations at the national level and some left to the university. Private institutions have some regulations, but largely make their own decisions.
A university is an expensive place to operate. Even public institutions get only partial tax funding. Tuition is designed for two purposes. One is to have the students contribute financially to the costs, but the other is to provide an incentive for students not to waste their time and, by their presence, deny opportunities to others.
There are other concerns besides money. Your presence might not be welcome on a campus if you are not affiliated with it simply for security reasons. Trying to sit in on courses without permission might well result in a court order keeping you off campus. This is rare, but it happens. Your presence would then have legal implications.
As to the IP question here, there is nothing special about being a student vs a non-student with respect to IP rights. Students as well as non students have the same fair use rights. But note that such rights are limited by (varying) laws.
No one would be likely to get upset of a registered student shared their notes with you. You could use them to educate yourself. But neither you, nor the student could, for example, republish them.
Most universities have rules about auditing. They may permit it at lower cost than a "matriculated" student, since there is less paper work, hence lower costs. You get an education, prodded you do the work, but you don't have a record of it. But it isn't "free" in any sense. Space in a classroom costs money, both directly, and indirectly since a seat occupied by one person isn't available to another.
Even in COVID times, when physical space isn't a factor, the ability for a professor and other course staff to handle students effectively is limited.
To be explicit about another of your questions, what you are really "buying" with your tuition is opportunity. Opportunity to learn under the guidance of experts who have the perspective to know what is important in their fields. Some students pay tuition and don't really take advantage. Sadly. But freeloading off of the system will deny opportunity to others who might benefit and be more willing to participate fully in the system.
Let me give a bit of other perspective. I'm a Tai Chi student and instructor. The art, as a martial art, is about 800 years old, though the principles are much older. We have a tradition that we don't teach for "free". We believe that we are giving something valuable to our students and so require something valuable in return. In China, in the old days, it might be a dozen eggs, or service on the family farm, but something. Again, this is for two reasons. One is to support the instructor, but, more importantly, to incentivize the student to think of the instruction as being valuable.
Another thought. There is currently a move underway to make university education, up to some level, free of cost to the individual in the US. That doesn't make it free, as tax monies would be required to take over a much larger share of the burden. I support those efforts, but the question about student incentives under such a system is something that should be considered. The current system, however, is blatantly unfair since the distribution of wealth in the US is so unbalanced. Hopefully we can work this out.

Thank you for the answer. Do you know of any official university policies that say that tuition buys opportunity?

Also in terms of your Tai Chi point, assuming there is full enrollment, don't professors get paid regardless of who comes? Adding non-disruptive online freeloaders would extend the reputation of the professors, and might bring new perspectives to the class

"provided" you do the work?

Frequently, material from courses is available to all for free. For example, you can take Benedict Gross's course on abstract algebra, Michael Sandel's course on justice, or Jim Hefferon's course on linear algebra. All have reputations as outstanding instructors, and these are just three of many examples.
Auditing a course means entering into a formal relationship with the university -- i.e., paying them. If you do this, and perhaps if you only unofficially "sit in" -- then the professor might be willing to give you feedback on homework, and/or to answer your questions. This will probably be at the discretion of the individual professor.
This is very worthwhile -- but there may be appealing options available for self-study if you can't or don't want to pay.

IME, "auditing" means you don't get feedback - because that's what takes up the professor's time. Maybe they're more willing to grade in small classes.

“Auditing” usually only involves coming to class and possibly access to course material.  Even if enrolment as an auditor comes with a fee, the student is unlikely in my experience to be guaranteed any feedbacks.

@AzorAhai-him-, ZeroTheHero -- Thanks for the correction. I looked at my own university's auditing policy and was surprised to learn that you are right. So I edited my answer. I still partially stand by my earlier answer though -- although maybe I've just been lucky myself in the past.


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Do German universities consider high school grades?
Do German universities consider the high school grades for post-graduate admissions since they ask for it?

It goes on like that. I had to prove being qualified for university access with the high school certificate before I was admitted for the PhD defense. Just do not think about it too much. If the grades were of any sigificance you surely would know. It would be made transparent.

Generally no - though high school grades tell you something about people (e.g. getting the very top grade requires hard work/discipline, while having very good grades can be achieved by being smart but lazy).

In theory there is no way to prevent them from doing so, but in general they will focus on more relevant things like bachelors degree.
The reason they ask (apart from the German love for bureaucracy) I believe is a weird quirk in German law. In order to study at a German university you need a "Hochschulreife", i.e. the qualification for university studies. This is normally gained by finishing high school.¹ It is however not gained by having a university degree, even though it is technically needed to get one in the first place. So in order to gain admission into a masters program, you both need to prove that you have the prerequisite bachelors degree, as well as the general qualification to study (i.e. have finished high school).
¹The specifics are a bit complicated, as not every type of German high-school counts. For foreign systems, I believe there are endless lists of what is equivalent and what is not, but in general this is not a high hurdle.

"German love for bureaucracy" Well, not exactly how I would put it...

I'd frame it a bit more positively: It's a way of making it a bit more difficult for people who managed to get into university (or any other kind of qualification) by cheating on prerequisites to continue without ever being asked for those prerequisites.

Odd.  In the US, finishing high school is not necessarily required to study at a university, and there are plenty of people walking around with PhDs who did not finish high school.

@AnonymousPhysicist Well, you have to decide somehow who is going to be admitted.

@AnonymousPhysicist Well, there is of course a long list of exceptions and about of 250 years of historical development of the system that explain why things are the way they are. But the details would be a bit far from the heart of the question.

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Do PhD Committees separate applicants based on whether they are a fresh undergrad or have MS/Work experience? (USA)
Does the PhD admit committee look at applicants differently based on the number of years they have invested?
Example:

Set 1: Undergraduates directly applying
Set 2: Master's applicants
Set 3: Undergraduate plus Work Experience

Set 2 and 3 are obviously way more experienced than simple undergrads. So is there any striking differences the committee tries to search for, or are there pre-defined number of seats for the various sets?
Or is all looked at the same? If so, is that really a fair judgement?

I ask about the fair judgement because it doesn't seem fair to me on a personal level and is just a personal opinion. Please do correct me if I'm wrong.

Unfortunately, life isn't fair. I doubt that committees separate applicants in this way. They want the best for the job, and if someone's work experience is relevant to the PhD (especially if it's experience doing research) then they are likely going to be the best for the position. However, it is becoming more common to consider mitigating factors; for example, someone coming from a disadvantaged background or developing country may not have had the same opportunities as other candidates, and this may be taken into account.

Thank you for the honest insight! Hoping for the best anyways :)

If a university were to do that formally, I hope (and suspect) that they would say so. But you can't account for individual preferences in such things. And, I'll also guess that individual bias cancels out in such committees.
Some professors might prefer to admit a student or two who they think might finish early, freeing up resources. Some professors might prefer to have students around for a longer time so that they can get to know them and also have more of an influence on their future.
Work experience might be a plus, but some early research experience is a stronger plus. Work in industry isn't generally a good indicator of success in research, though there are a few exceptions.
But even a student admitted with an MS/MA has to pass qualifying/comprehensive exams, so, in the US, entering with a masters may not bring a big advantage. They also have to choose an advisor with less information since it is sooner. This works well for some, but not all students and professors recognize that in the admission process.
I think that the most important thing, far outweighing all others, is whether the committee can make a fairly accurate projection that admitted students will succeed, both in the degree and thereafter. This is one reason that letters of recommendation have quite a lot of weight in admission decisions and can overcome some deficiencies.
But, for a direct answer, no, there is no strong preference for any of the groups you list.

Thank you so much for this answer! Really gave me a good idea about what to expect!

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Under Review status vs Decision Pending (Taylor & Francis journal)
In the ScholarOne system (one of Taylor & Francis journals), the manuscript status is "Under Review". However, under the regular submission system, the status is "Decision Pending". Which of the two instances is correct?

How would it help you to know? It's pointless to obsess over submitted papers.

The paper I published recently was submitted through ScholarOne system, and based on my experience, after the review before editor's decision, the status remains under review. Recently, I learnt that the submission can also be done through the Taylor & Francis website, and there when the paper returns from review it shows decision pending (waiting for editorial decision), while in the Scholar One system it shows under review. I am experiencing the same thing. But what I understand is that the experts review is completed awaiting editor's decision. So the manuscript status "decision pending" and "under review" can be the same.


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IUBH university Msc can give a chance to have a phD in germany?
I came accross a Masters of Data Science from the online IUBH university in Germany.
Would this degree grant me the chance to pursue a PhD in Germany? or will it be looked over as a weaker university or a degree with little research experience ?
and if not, does anyone know a better program that would help me through this ?
some background information about me:
I have started working in Germany in the Hardware sector for about 3 years. Almost a year ago i switched to Data Science because i felt i much more motivated working in that discipline. I have a Bachelor of engineering degree which had me study 5 years, granted me the ability to work in Germany (since it has more credits than a Bachelor of science engineering degree) but not a masters degree. It has always been a goal of mine pursuing a PhD, but unfortunately i cannot pursue a Master's degree in Germany without leaving my full time job, which i need to support my family.

The IUBH is not a university, but a "Fachhochschule" (somewhat misleadingly translated as "University of the Applied Sciences" into English). The expected qualification for enrolling into PhD studies at a German university is have a Master from a university. While exceptions to this are possible, degree programmes at Fachhochschulen are meant to prepare for work in industry, not in academia.
The leading distance-learning university in Germany is the FernUniversitaet Hagen (https://www.fernuni-hagen.de/). Their MSc degrees should fully qualify your for subsequent PhD studies. (I am a Hagen-alumnus, and went on to do a PhD in Cambridge after getting my MSc Computer Science from Hagen).

I've had some experience working with people at FernUniversitaet Hagen (also in CS) and recommend them highly.

Thank you for your answer, that really helps me a lot. I checked their programs and they only have computer science in german after having a C1 level.
That is really much higher than my current level. do you happen to know any other programs that might offer this in english ?

@anxiousPI There is no reason to do a degree at a German university in order to be admitted for a PhD if you are planning to do it remotely anyway.  Note that it might also be possible to be admitted for a PhD with only a bachelor's degree (though very likely you would be obliged to take some extra courses and/or hand in a master's thesis).

Arno, I think I remember reading about you on the news, very impressive. I can personally vouch for the mathematics master as well (which is better suited for someone wanting to become a data scientist probably), their course material is imo. better than that of most other German universities. Since a masters degree is basically required to start a PhD in Germany and Hagen is the only remote option I'm aware of that is fully recognized, rigorous and cheap I think @anxiousPI will have to bite the bullet and become fluent in German.

Sorry but your answer is incorrect. You can do a PhD in Germany with a Masters from a University of Applied Sciences, legally they are the same kind of degrees as Universities. You only need to make sure that is is a scientific Masters program, there are many of them around Germany.


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Can we study University level subjects without getting admitted into a university?
I am currently a senior high school, and next year I will enroll for my undergraduate studies but I am afraid that my grades would not be good enough  to be admitted in good universities like MIT, Princeton etc.
So can I study advanced topics like general relativity, quantum mechanics etc., like at university but without getting into it?

You can always self-study, but you won't have the support network a university offers you (exercises, tutoring, structured lectures).

Do you mean self study? Your abbreviations don't register with many of us. What is GR, etc? Why focus on such a narrow range of universities. I think the US has over 4000 colleges and universities.

Getting into MIT or Princeton is not the be-all and end-all. A perfectly good education in physics (and any other field) can be had at hundreds, if not thousands of universities around the world.

This past year, MIT admitted 7.3% of applicants across all programs. The implication is that, relative to the number of college applications, essentially no one gets in to MIT, most because they assume they can't and don't apply.

Besides using textbooks for self-study, note that MIT provides video lectures for many courses at https://ocw.mit.edu/courses/physics/ for free. There are plenty of such resources online also from other institutions.

@Polygnome, perhaps you can expand that a bit into an answer.

Why do you think that "advanced topics like general relativity or quantum mechanics" are not taught at schools that aren't the best in the world? I would assume every well-respecting university with some sort of graduate program will have an offering of advanced courses on at least a selection of the subjects that interest you.

My main intention is that I wanna make a back-up plan that at worst case if I don't get admitted to any universiry how would I continue my education.

What do you want to do in life? what are you trying to achieve by studying "advanced topics like general relativity or quantum mechanics"

To explore secrets of the cosmos.....

I'm confused.  You say that you are  "afraid that my grades would not be good enough to be admitted in good universities like MIT, Princeton etc".  That would indicate that you have near perfect grades.  Then you say "wanna (sic) make a back-up plan that at worst case if I don't get admitted to any universiry (sic)".  There are a lot of not quite top tier places that will admit folks who don't make the cut at top tier places, and a lot more places below that on the university rankings. One thing to explore is a year at a junior college before transferring.

Question: Are you a student in a US high school?  If so, you really need to work on spelling, grammar, and so on.  If you're an international student, good TOEFL scores may help, otherwise "MIT believes that students in any field should learn to write prose that is clear, organized, and eloquent, and to convincingly present facts, data, and ideas."  https://mitadmissions.org/tests-scores/

There are plenty of homeless people who went to Ivey league schools, and plenty of people who started off in community college who have gone on to do greater things than any of us. Don't limit yourself just because of the school you can get into.

This is a response that takes various comments of the OP into account rather than an explicit answer to the question asked - but it is too long for a comment, and I really think that the OP should be made aware of the following points.
@OP:
I do not intend to be rude, but I would strongly advise you to recalibrate your expectations and your perception of how research and academia work. For instance,

you say that you never managed to get good grades in highschool, but your question focusses on "advanced topics like general relativity, quantum mechanics";

you are worried (in some of your comments) that you won't be admitted by any university, but your question focusses on places like MIT;

in another question you mention research of yours (which I find a bit odd, anyway, since you write you're a highschool student) and don't seem to be particularly convinced of its quality, but in a comment here you claim that you wish to "interact with greatest minds of this world".

Now, it is important to note that none of your goals is completely unreasonable in itself: there are, of course, a lot of potential reasons why a smart student might have poor grades in highschool, and might anyway master theoretical physics later on; it is, as mentioned by others, also absolutely possible to do your undergraduate studies at a respected but not-at-all famous university, and then do your graduate studies at a very well-known place; it is also possible to start out with not particularly good research and to improve quickly and considerably, so that the "greatest minds of this world" would like to discuss your research with you.
However, the only way to achieve any of this is to keep a realistic perspective and to move forward in small and down-to-earth steps.
Currently, your contributions here merely focus on extremes ("bad grades in highschool vs. studying advanced topics in theoretical physics"; "not admitted to any university vs. admitted to MIT"; "research of low quality, produced as a highschool student, vs. interacting with the greatest minds of this world.")
Here are a few suggestions of a more realistic approach:

If you had difficulties to earn good grades in highschool, make a thorough (and honest) analysis of the reasons, and try to figure out what you can do to improve this situation when you attend a university. In order to get any degree you will have to pass exams, too, and if you want to have any chance of your dreams coming true, you will have to do very well in most of them.
If you had poor grades in highschool, this might also indicate (though it is not sure, of course) that you don't know well some of the material from highschool. No matter whether this might not be your fault or what the precise reasons are - it might still pose a problem when you want to study topics in physics at university level. So please try to find out whether you have, for instance, serious gaps in your highschool knowledge of mathematics or physics (and maybe also some other subjects that could be relevant), and if you find some, try to close these gaps before you're heading towards more advanced topics.
(Please note that much more basic physical topics than general relativity and quantum mechanics - for instance, classical Newtonian mechanics - require mathematical knowledge which goes far beyond the mathematics taught in highschool.)

If you intend to become, in a few years, a graduate student in one of these "top-tier" universities, try to make choices right now which can help you get admitted then. For instance, make an effort to find out which kind of undergraduate experience (for instance, research experience, but also other things) are considered advantageous for the admission decision, and then try to choose a university for your undergraduate degree where you have good chances of acquiring this experience.

Getting involved with research early is certainly a good idea of you have ambitious plans - but the most reasonable way to do this is within the setting of a college or university and in collaboration with other people who already have experience in doing research.

Please try to inform yourself about some details of the academic system. For instance, you write in one comment that you are considering self-studying, then to write a few good research papers and to get a PhD in Cosmology. As mentioned by other users, this is a very unrealistic plan:
First, being admitted for graduate studies seems to be very unlikely if you do not have an undergraduate degree. So if you want to do a PhD, there is most likely no way around getting admitted for undergraduate studies first.
Second, producing good research and getting it published in reputable journals is very, very difficult if you do not have any formal education (= education at a university) in your subject and no senior colleagues that support and advise you. Producing really excellent research and getting it published in top journals (which would fit your, in some respects extremely ambitious, goals) is literally impossible without the aforementioned prerequesits.

Now, all these suggestions certainly come across as much less glorious and prestigious than getting admitted to MIT, or studying general relativity as soon as possible, or interacting with great minds. However, please be aware that even the greatest minds spend a considerable amount of their time with completely non-glorious, down-to-earth routine tasks (like advising students, marking exams, writing grant proposals, and so on).
Also, even if someone is born as a genius, a degree from a top university, a solid understanding of theoretical physics and the possibility to work with great people do not simply come to them out of the blue - even the smartest people have to work long and very hard for this, and they do it by taking many - maybe amibitious, but most often still small and realistic - steps. So precisely this is my advice for you.

(+1) Super! Several of these non sequiturs, although definitely not ALL that you've pointed out, were going through my mind as I read the question and comments, and I was debating whether to bring any up in a comment, and then I read your answer.

Great answer, well-written and far better than mine, I hope the OP digests it and puts it to good use. I'd echo Dave as well. +1. My one quibble is you write "Producing good research and getting it published in reputable journals is very, very difficult if you do not have any formal education" - it's also very, very difficult if you do have formal education. :) Effectively impossible without...

@BryanKrause: Thanks for your comment! I suspect I had a slightly less restrictive picture of "good research" and "reputable journal" in  mind when I wrote this sentence. If the research shall be good enough and the journals sufficiently reputable to achieve the OP's very ambitious goals though, then I completely agree with your assessment. I'll edit my answer accordingly.

I'm very curious to know what OP considers "poor grades". The same grade might be great for someone aiming to just get the degree and an utter failure to someone who expects straight A's.

@Lavertu poor grades is approx 50% ~2 GPA.

Honestly speaking, yes my plan is very unrealistic. I have decided, that I will try to get master degree from any university and until my graduation I will try to publish a breakthrough research paper in the field od theoretical physics- I have few ideas on SR. And I hope that  the breakthrough will help me to get a job and ph.D along with my master degree.

For gap in knowledge part.... That's not problem, I am learning all the prerequisites and other topics like Classical mechanics, electromagnetism, Special Relativity, etc.... And trying my best to acquire continuous knowledge. And I mentioned MIT, Princeton just because I want to self study at that level such that my knowledge is comparable to a MIT student......

I have been failed in publishing two research papers so I am aware that it's difficult to do....But I have ideas and very very very big dream.

@SwayamJha: I appreciate your enthusiam. Still, your comments make me reiterate the main point of my answer: PLEASE do yourself a great favour and take it step by step. Starting out as an undergraduate student and planning to write a "breakthrough paper in theoretical physics" is just not how the game is played. Given the information you provided, it is quite save to assume that, by now, you simply do not have the necessary knowledge to even compare any idea that you might have with the current state of the art - let alone to judge whether it has the potential for a breakthrough.

Please note that it is not my itention to discourage you. Quite apparently, you have a lot of enthusiasm for science. But in order for this enthusiasm to be fruitful, you will have to take it slowly first and focus on goals and events which you can realistically influence with your current decisions. Aiming to publish a breakthrough paper before your master's degree does not belong to this category.

On the other hand, figuring out the research focus of various universities, as well as the possibility to do undergraduate research there, checking how much those universities fit your personal needs, applying to many of them, and then starting out by first focusing on your undergraduate studies (rather than planning to write breakthrough papers somewhen in the future) does belong to this category.

Taking up challenging tasks can be a good motivation, of course; but I promise you that, for the first few years, you can find a lot of good challenges (and, hopefully, a lot of fun, too!) with only studying what is already known. The "secrets of the cosmos" (to quote one of your comments) are, like all real secrets, quite persistent - they'll still be there for you after you've focussed on a solid undergraduate degree.

"For instance, you write in one comment that you are considering self-studying, then to write a few good research papers and to get a PhD in Cosmology. As mentioned by other users, this is a very unrealistic plan" It's basically a recipe for getting yourself considered a crank and then de facto getting blacklisted from academia.

@SwayamJha "I want to self study at that level such that my knowledge is comparable to a MIT student". Physics is the same no matter where you learn it. There aren't secret bits that they only teach at MIT. Such universities are prestigous due to their research output, not because they teach more topics within a field or more difficult topics within a field than other universities.

After a year I read my question and this answer again and realised that my expectations and plans were really impractical!!! Thanks alot for all of your guidance.

@SwayamJha: You're welcome!

There is nothing to prevent you from self-studying topics in physics (or any field) before you go to university, during your university studies or after you have graduated. As mentioned in the comments, there are many lecture courses freely available online which could help you in such an endeavour.
However, as a physicist myself I would caution you against jumping straight into learning general relativity and quantum mechanics on your own. These are advanced topics that would typically be taught towards the end of an undergraduate degree, after at least two years covering things such as classical mechanics, Newtonian gravity, special relativity, optics, electromagnetism etc, and probably a number of mathematics courses too (this is country-dependent but probably at least algebra and calculus at a higher level than you learned at school).
Furthermore, there are a huge number of benefits to studying at a university instead of on your own. For starters, the degree programme is structured for you so that you don't have to work out all the different bits of physics and maths you need to understand from one topic before moving to the next. You also have the chance to ask questions during lectures, you will have access to a library, be set assignments that you get feedback on, thus allowing you to gauge your progress and you will be surrounded by people studying the same thing, who you can work with and learn from.
Beyond studying for a degree, going to university is an important "coming of age" experience for many people, as you'll probably live independently for the first time, meet many new people, get the opportunity to try out new sports and hobbies, move to a different part of the country etc. So by self-studying you will miss out on all of these important and fun milestones.
Finally, as I said in my own comment, going to MIT or Princeton is not the be-all and end-all in life. I had ambitions to study at a top university for my undergraduate degree that never came to fruition. Instead I went to a tiny university that hardly anyone has ever heard of (it's certainly not reputable for physics) but I am certain that I enjoyed my degree far more and got far better results than I would have if I'd have gone to a top university.
This is because the atmosphere was more laid back, there was a cooperative rather than competitive atmosphere amongst the students and the physics department was really small, meaning that I got to know all my course-mates and lecturers really well. This was infinitely preferable (to me) than suffering through a tough degree for four years on a course where I knew no one and was just a face in the crowd to the lecturers.
In summary: by all means you can study topics in physics without going to university, but I would suggest starting with a less ambitious programme. You don't need to go to a "top" university full stop, but you especially don't need to go to one to learn advanced topics. GR and QM are taught as standard in every reputable physics degree.

Actually, I am finding a back-up plan that at worst cases I can train my mind and acquire knowledge of graduation level without university and then try to publish few good Research papers which may help me to get P.hD in Cosmology.

@SwayamJha I would say that it is impossible to get a PhD in cosmology without having a degree in physics. Even if your self-taught knowledge is the same as the content covered in a degree, no university will admit you for a PhD without proof of prior academic qualification. This would typically be a BSc or BSc + MSc depending on where you are in the world.

Furthermore, publications are not a prerequisite for admission to PhDs in cosmology (source: I am a cosmologist). You will be much better off studying diligently, getting consistently good grades across your physics degree and working on a small research project (possibly in cosmology but it's not necessary) towards the end of your degree. Build good relationships with lecturers so you will get good reference letters (see again my point about the benefits of studying in a small department/university).

@SwayamJha While it is theoretically possible to get admitted to a ph.D. program without having attended a university (and in fact it did happen in the past), it is extremely hard. Harder than "once in a generation" hard. I strongly urge you not to consider it a viable option.

@SwayamJha In case you want to do some self study here are the topics I studied in my first year: calculus 1, special relativity (not general relativity!), Intro to classical mechanics, statistics + Lab work, calculus 2, electromagnetism, waves and optics. It's better to build to build a good foundation in these rather than losing your mind over general relativity. A little preparation doesn't hurt but you will have a hard time if you try to do an entire study on your own. What's wrong with a university that's not MIT?

Frame-challenging a bit, because the question seems to be originating from fear of not being admitted to a "top" university, rather than a focused interest in self-study.

There is little direct educational benefit to enrolling in MIT, Princeton, etc as an undergraduate rather than, for example, well-respected state research universities.
There are some possible side benefits, like A) You're attending classes with other people admitted to MIT, Princeton, etc, so you may find more competition that drives you, B) You have a chance to network with people who have "connections", including fellow student, alumni of the institution, and various visitors, and C) You get to put a "fancy" name on your resume which might make people more likely to read your resume and maybe even hire you/admit you to graduate school based on the name of the school you attended.
There are also possible downsides. Professors at the "top" institutions may have less time for individual undergraduate students (and even grad students) than professors at respected-but-less-prestigious institutions.
Importantly, all of these factors are also incredibly individually variable.
Self-study is okay, but I don't think it's a good serious learning path for most people (certainly fine to pursue as a hobby, but you'll lack the support and external motivation that being enrolled in official courses provides; you'll also lack connections to research opportunities). It doesn't sound like you are particularly interested in self-study, but rather that you are looking for a backup plan if you aren't admitted to your preferred schools. There are lots of good institutions where you can learn about relativity and quantum mechanics: don't limit your search to MIT and Ivys.

@Libor Even then, your advisor matters more than the name of the institution (of course the two can correlate).

I think that quite a large fraction of liberal arts colleges are fine places for an undergraduate degree. You don't need to attend an R1 and may well get much more personal attention at a smaller place. Not cheap, though.

@Buffy Yeah, in biology, I'd more strongly recommend R1s when possible because A) State R1s are not actually particularly selective for undergraduates (generally speaking), and B) undergraduate research experience is super important if you want to do grad school, and these experiences are quite a bit more limited at liberal arts schools (though they do exist, and I went to grad school with plenty of people from those schools; some of them had to do more work to find research experience outside their school). Probably a lot less important in math, not sure about physics.

And for some fields (biology, physics...) access to lab equipment might be essential for a beginner. More or less impossible for self study and possibly limited at (some) liberal arts places. For high energy physics you probably need a lab (guessing, not my field).

Yes you got me right. I am finding a back-up plan as I mentioned I never manage to get good grades(for few reasons I don't want to mention). So I just wanna know, if at worst situations no University alllow me then can I self-study at that level- as my dreams are very big.

And actually, I do like to self-study as there is not any sort of so called restrictions like in schools and collages.

@SwayamJha Seeing your comment on another answer that you want to publish some papers...if that's your goal, definitely do not do the self-study path. It's extremely hard to succeed that way, I'd say effectively impossible. We regularly get questions here from people trying to publish on their own without support; there are very few good answers for what they can do. Don't get stuck in their spot. Find a university that's a good fit for you, and study there.

@Bryan I would not select the self-study path myself as I wanna ti learn and interact with greatest minds of this world like Brian greene, Walter lewin, Alan guth, Leonard susskind(and all whom I admire) but for ths "worst" case I have to make plan so that I can continue my quest independent of universities. But I will try to enroll in any university.

@SwayamJha Ok, well there is a very very big gap between "not admitted to MIT" and "not admitted to any university". If you did find yourself somehow in the "not admitted to any 4-year university" you're still better off starting in a 2-year program and transferring to a 4-year if your goals are as you state, rather than self-study.

Okay thanks alot for your consideration and time.

I wanna ti learn and interact with greatest minds of this world like Brian greene, Walter lewin, Alan guth, Leonard susskind --- Even if you get into MIT, Princeton, Harvard, or whatever, you're NOT going to be interacting with those people, not unless you're a once in a decade type person for that university, and probably not even then.

@SwayamJha Walter Lewin is retired and no longer at MIT. Susskind is 80, Alan Guth is 74, and Brian Greene is probably busy performing on some TV Stage or writing a book rather than available to chat in his office at Columbia. Just saying...

There are also many reasons for NOT trying to get into one of those "top" universities.  Foremost among them is money: if you don't have either wealthy parents, or the qualities (not all of them academic) needed to get a full-ride scholarship, then how will you pay tuition & living expenses?  Going to a state school in your home state (if you're a US resident) is going to be significantly less expensive.
Second is quality of life.  Admittedly this is subjective, but you do need to consider what your life will be like outside of class & academic work.  I suppose MIT deserves its reputation as a great school, but the downside is that it's located in the Boston metro area, which is IMHO the pits.  Same is true of most top universities: I did my first year at a fairly high-ranked school in a largish urban area.  Academically it was fine, otherwise the place was an invitation to either alcoholism, depression, or suicide.
Likewise, if you have a good, supportive family, you may do much better choosing somewhere close to them.  Or if your family is of the other kind, a place as far away as feasible may be a better choice.
Finally, as others have said, where you do your undergraduate work is not nearly as important as how well you do it. It's quite possible to get into a graduate program at one of those top schools with an undergrad degree from your local state university.  It's also possible to participate in interesting research programs and/or remunerative industrial jobs with a grad degree from those state universities.


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Can a university revoke my degree for not attending classes?
I have a 60 hour work-week due to work/school/commuting/homework, so I've had to make sacrifices -- usually this is attendance of mindless gen-ed classes. I'm worried that the university may revoke my degree if this comes to light.
Described in the answers to this question, a university can revoke a degree if it is found that the student broke the code of conduct during the course of the program. My university's code of conduct specifies that it is up to the instructor to determine attendance policies, and AFAIK none of the classes I have skipped had clauses that resulted in a failure of the class due to poor attendance (just grade penalties). Despite this, would it be unprecedented for the university to claim I was in violation of an attendance policy anyway and revoke my degree? I'm worried the school may see this as an insult and retaliate.
If it matters which classes and how severe, I skipped 50% of Physics II and only attended 4 days of Calc II (test days). I plan to do the same with Chem I this semester. I was not at risk of failing the courses. I am pursuing a bachelors degree of Computer Science at a US university. I have never broken any laws or cheated. I am in good academic standing and on-track to graduate at the end of the semester.

Some (government) funding in some countries is linked to attendance as well as grades / performance - once a threshhold is passed then a visa can be revoked which means effectively out of the course...

What’s “gen-ed” and in what way is it “mindless”?

@KonradRudolph non-major classes, and mindless in the sense that I can show up 4 days of the semester and not flunk out of the course :P

@Drew Just to clarify: are you saying you’d not learn anything useful even if you attended? Or that you can wiggle your way through the exams despite not attending because the exams are lax? Because that impacts the answer: the minors I took formed an integral part of my education, I’d regret to have missed them (extenuating circumstances notwithstanding).

@KonradRudolph Would rather not start a political discussion over what's valuable and what's not -- off-topic form original question anyway.

@Drew Fair enough, my previous comment was wrong to suggest that this would change an answer (this was accidental, promise). It would change whether I’d recommend you drop these courses but that’s indeed off-topic and you seem to have your mind made up.

It would depend on the university.  Go to class is a good indication of what will be on the exams.

@KonradRudolph pretty sure "gen-ed" stands for "general education", the kind of non-major course that universities make students take for breadth requirements.

When I was in school I had several friends who would only show up to class on required days (test, presentations, etc). Unless the instructor communicates that attendance is required, it isn't.

How do you imagine the university finding out you skipped classes?

If you don't know whether or not if "classes I have skipped had clauses that resulted in a failure of the class due to poor attendance"... what can anyone else tell you without a copy of your syllabus?

FWIW, I was in your situation when I was in college. I worked a lot and took way too many classes. I think if I had it to do over again, I would have just taken on more debt and lightened my load during college. It might be worth cutting back work hours now in favor of school hours. You'll have plenty of time to work when you graduate and it'll probably be both more interesting and remunerative than what you're doing now

Do you mean "withhold" or "revoke"? It's not "revoke" if they haven't awarded the degree yet.

As a bit of side note, have you considered trying to enroll in some online classes that don't require physical attendance? Particularly for gen. ed. classes? (You might even consider investigating if you can arrange to take them through another college and have the credits transferred.)

@jpmc26 I've taken a few, and the workload of online classes is usually greater than that of in-person classes. The frequency of assignments is much higher, and there are weekly mandated discussions (versus showing up to an in-person class and not saying a word). I'm guessing it's because online classes have to have more concrete evidence that they're teaching students, which is fine, but doesn't work out if you're trying to save time. As for transferring, I don't think the college is the problem -- the classes themselves aren't too difficult

It is part of the cultural norms of American universities that your attendance or lack thereof is an issue for each individual course instructor to pursue or not pursue as they choose.  At my university the administration is involved precisely insofar as to have the following policy:

Students are expected to attend classes regularly. A student who incurs an excessive number of absences may be withdrawn from a class at the discretion of a professor.

This states the situation well: the administration empowers the instructor to penalize the student for poor attendance, including withdrawing them from the course. Thus whether and how your lack of attendance in a course is problematic is between you and the instructor of that course.  You seem to be worried about attendance that is acceptable to the instructor -- more precisely, not resulting in failure or withdrawal -- but is somehow unacceptable to the university as a whole, since you write

Despite this, would it be unprecedented for the university to claim I was in violation of an attendance policy anyway and revoke my degree? I'm worried the school may see this as an insult and retaliate.

In a word: yes, this would be completely unprecedented and moreover implausible.  First of all, how does the university even know about your attendance?  Even if they somehow found out (maybe you write an editorial in your school paper advocating attending class as little as possible?!?) it would widely be viewed as a violation of the instructor's rights to penalize you for lack of attendance when the instructor did not.  Finally, you speak of a degree being revoked which means that first you get it and then they take it away from you.  Degrees are only revoked for the grossest forms of academic misconduct.  It would be outrageous for a university to revoke a degree due to lack of attendance -- frankly, that would reflect very badly on them and would invite censure and possibly even legal action, as it seems manifestly unfair to conjure requirements retroactively.
Summing up: you should clear your attendance plans with each course instructor in advance.  To do otherwise is really not safe, as you can see that e.g. my university (which is not so far away from yours) empowers me to withdraw a student for sufficiently poor attendance.  If your attendance plan is okay with the instructor, it will be okay with everyone else too.

Completely correct answer. For what it's worth, my (U.S.) university's policy regarding attendance is virtually identical to the one you've stated here.

At University I had many lecturers (UK) who were useless at lecturing and I was useless at mornings, but they wrote wonderful lecture notes, books, and practicals (and were mainly there because they were leaders in the field, but often had limited social skills, lovely as they were). I didn't attend those classes regularly and probably they liked the low attendance, too. Teaching is teaching, more power to them. It's important to stay in touch somehow, though, as there may be requirements for practicals, etc, you only hear about in lecturers, so you need friends to help you out occasionally.

Early in my undergrad education, I had a Differential Equations lecturer who had terrible English skills (nor did I speak his native language). The lectures were an absolute waste. But out of respect, I attended class and spent the time teaching myself (referencing the textbook, taking notes, and effectively learning DE solo). It was the closest I could get to gaining anything from the lectures. In retrospect, I should have attended the lectures, and feigned paying attention, then taught myself after class.

Assuming you haven't been awarded a degree yet, you can't have your degree revoked.
As for whether the university can refuse to award you a degree because you didn't attend class - key point to note is that university isn't high school. University students are generally treated as adults, and adults are free to do what they want, including miss class. It comes down to whether you can meet the stated requirements for the course even if you miss class. If you can, then sure, go ahead. Missing class isn't the same as the situation in the question you linked - that involves cheating by not actually meeting the requirements, but giving the impression that you did.
Caveats: by not attending class,

Your lecturers can't write you recommendation letters since they have no impression of you.
You miss anything that's said in class, e.g. the lecturer might mention an interesting fact that's never examined for, but would've helped you five years in the future.
Some lecturers might have attendance requirements.

This is under the assumption that I am awarded the degree (I am on track to graduate at the end of the semester). Sorry for not clarifying -- I will edit it into the question.

+1 Just to emphasize the key point -- you cannot lose your degree for violating a policy that doesn't exist.

On the other hand, most employed adults will find that frequently not attending their jobs will definitely get them fired very quickly. That not attending the social functions of their friends will weaken the friendship.  That not attending your daughter's dance recital is an easy way to end up sleeping on the couch and making your daughter cry.  So I don't buy the whole "we treat them like adults in Universities" logic.  All this means is "we encourage them to treat the university as an unimportant trifle without consequences".

@zibadawatimmy I use that phrase to mean that the university treats the students as people who are capable of making decisions and taking responsibility for it, so e.g. if you miss class and fail, they're not going to let you take the next class on the way to the degree since you failed the prerequisite. But if you can miss class and still pass, more power to you.

@zibadawatimmy The comparision is unfair, as the "treat as adult" part means, that the university often declares the attendance as completely optional, relying on you to judge if you need to be there or not. Being not there and investing time in reading more books is a completedly viable option. A good reason may be a schedule, which makes it hard to be at the university, but allows for enough time to read about the topic. As an adult you should know, that you probably will need some of the lectures. On the other hand you should know, that you do not need 100%.

This answer misses an important subtlety: Some university instructors do impose attendance requirements on their courses, either explicitly or implicitly through the including of "participation credit" or in-class quizzes and the like. Thus, it is entirely possible for a student to fail a class, despite meeting all other course requirements, because they did not attend class, or even because they missed more than a trivial number of classes.  And if that class is a degree requirement, the student won't get the degree.

I don't remember having taken a course with an attendance requirement - at most it was "participation is worth ___% of your grade". So you can still miss class. You'll get 0% for participation, but if the rest of your grade is strong enough, you'll still pass.

@Allure That doesn't mean it doesn't happen. My friend TAs a class where 4 absences is an automatic fail. It causes him no end of headaches.

It might be worth noting that some universities or programs have their own attendance requirements. In the USA most law schools have fairly strict attendance policies they impose on the entire school because they are ...encouraged to do so by the ABA.

@Allure: As always, institutional practices vary widely. At my community college, it's required by the department that instructors enforce the max-4-absences-or-fail policy in all remedial courses (~100 sections per semester).

FWIW, at all the service academies, attendance is mandatory.
For your specific college, if a professor makes it mandatory to attend and you don't than he can flunk you.  If you need the class, than no degree.
You might like it, but that is likely how it would play out.


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Can I still publish a paper on peer reviewed journals several years after publishing it on ArXiv?
I have done some discoveries concerning signal processing from about 6 years which I think are quiet important advances but I never have time to finish the works. As example I know that the main application are new on my field but I am not sure the theory does not exists on other fields. The links with other theories are not fully established yet, so I do not know exactly what is new and what is not. I do not want for now to be judged by peer reviewers which risk to only examine what is bad on the paper but I found it a pitty to not share those discoveries so I am thinking by submitting as preprint, and after some years and maybe some advices/correction from some readers, submitting it on a peer reviewed journal.
If I do that, and someone publish the same ideas after (particularly if they do not cite me, because they do imagine those ideas come from them or are obvious), will I still be able to publish it since reviewers can oppose me that those ideas are not new anymore ? Journals could not see the interrest of publishing works which are already known by the community on the only aim to help me to claim my anteriority.
So to sum up, if a reviewer reject a paper because the ideas already exist from other works but those works are posterior to the preprint, can I ask to editor to not take this opposition into account?
Is there examples of important papers published years after their preprints? In that case should it be adapted to explain what others have done of your works ?

You must choose (a) Submit preprint and concurrently submit to journal or (b) Submit preprint only. (a) requires more work and might lead to rejection. (b) has the problem that someone else extends your preprint and gets a publication and you can no longer submit to journal without citing them or without extending your preprint. You cannot have your cake and eat it too.

I guess you right but if I choose (a) and get continuously rejected it might become equivalent to (b). Thus unfortunately, the system incite me to still wait several years until I manage to make it in good shape and having enough hope to be accepted. However to be sure we will understand each other, I must add that I have no problem about citing other works coming after (on contrary it is even a kind of proof of interrest). I just do not want that those papers prevent me from publishing already published ideas and claiming my anteriority.

If some paper A publishes a very similar idea (a) without citing your preprint or (b) extends your preprint to novel directions, it would be hard to publish your preprint to a journal if the reviewers are aware of paper A, because (a) either the idea is already in A (& publishing a similar paper offers no benefits) or (b) paper A has a better contribution and your paper now seems like a step back. Also, if your preprint is in not "in a good shape" to be published, then nobody will cite it and with good reason. Presentation of a "discovery" is as important as the discovery itself.

You speak of ideas, yet ideas are worth close to nothing without results, at least in the academic understanding. Sure, they are the beginning, but are not intellectually protected by themselves. Anyone can have an idea, but it takes work to develop that idea into a solid contribution to science.
So, if you have real "discoveries" and "important advances", you shouldn't be afraid to submit them for peer-review, as that is the only way to scientifically validate your work. Otherwise, it doesn't matter if someone develops on your idea and doesn't cite you. Similarly, it doesn't matter where you put those ideas, it could be arxiv, your personal website, facebook, etc.
As stated in the comments, you can submit a preprint and also submit to a journal, the preprint puts a timestamp onto your work so you have time to publish it (even if it gets rejected and you retry). However, this holds only for work that has the chance to get accepted for publication, i.e. has some real contribution.

Thank you for you answer.To give more details, I do have clearly results on a specific field. they exceed by far those from any other methods even if this is a small application on the very wide range. I am pretty sure for now it will be rejected because links with other theories are not done, and I do not know exactly what is new and what is not inside. It is not so complicatied so it make it easy for someone to reuse the idea without citing it by considering this was obvious even in good faith. I do not care they do, I would just want that they do not prevent me from publishing and claiming.

Unfortunately, it seems trying to publish either on preprint or on peer-reviews is too risky for now and I guess I have to keep it secret until I finish it to have a good chance to be accepted.

You always want to put your best work out into the open. If your work is right now not of sufficient quality (as can only be judged by yourself) to be read and evaluated by peer reviewers, then one could argue it is also not ready to be a pre-print (where essentially all readers are your peer reviewers).
There isn't something magically different about peer reviews for a paper other than to make sure the paper doesn't claim what it shouldn't or can't and to make sure that the science is solid. Yes, this can lead to a prolonged back and forth between the author and the journal/reviewers, but from an author's perspective you always want to post/submit your best possible work with clarity of ideas, concepts and immaculate presentation of the data. Nobody wants the literature (pre-prints or peer-reviewed papers) to be littered with stuff that's not yet 'finished'. And as a scientist, you shouldn't want to let your good ideas go out into the world in a bad wrapping!
The fact that you struggle to find time to finish your work will be recognizable by many, but there are two options: you need to practice patience until you have time to polish OR prioritize finalizing it.

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


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How to overcome a mistake you make in your proof and regain motivation?
I am an undergraduate student in computer science, and I have been working as an undergraduate researcher in theoretical computer science for 7 months. There was this problem that my supervisor mentioned, and I worked on it for a while. But I only managed to solve a sub-case of the problem, which didn't interest my supervisor at that time. However, he wanted me to write a manuscript about it anyway. I put a lot of effort into writing it, but he didn't bother to read it. And we have moved on to other things.
A week ago, my supervisor called me, and he said that he found an interpretation of the sub-case of I've solved, that economists are interested in. And he said that we can publish it in a journal. So, I was really hyped. We met the next day, to review my proof. But when I arrived, I learned that a friend of my supervisor found an implicit assumption at the beginning of my proof which was clearly wrong.
As you can imagine, I was devastated. I've tried to find a workaround, and fix my solution, but I've just found another thing that I've overlooked. So I've lost my enthusiasm and self-confidence.
However, my supervisor claims he found a completely different idea to solve the problem. He explained it to me, however it has some parts to be completed. So he wants me to write a manuscript about it and fill the gaps. However, I cannot find any motivation to do so. I am overwhelmed by the feelings of failure and anger.
I know that I should be working on my supervisor's idea, but I'm so distracted with the mistake I've made. How can I overcome my mistake, and start to work again?
UPDATE: A month later, we solved the problem :)

Errorist, you are in a fantastic spot for personal growth. I am honestly excited for you right now. Encountering these sorts of issues and overcoming them will be an AMAZING life event for you. The fact that you can identify what is going on in your head and write them down like this is a big step. Do some more thinking about why you feel the way you do, and it may help you identify ways to overcome those feelings.

I also really like @user37208's answer, except for the last two paragraphs. Sometimes avoiding situations like this are impossible, and powering through emotions like those is nearly impossible. They are a part of life, and what you should learn is how to deal with them when they do happen. Because they will. When I get overwhelmed and discouraged, I have found that writing everything down on paper, and then creating a step-by-step list of what I should do to solve the problem helps immensely.

Possible duplicate of How should I deal with discouragement as a graduate student?

If science were easy enough that we never made any mistakes, there would be no sense of satisfaction or achievement when you succeed.  Take it as evidence that your research is non-trivial and hence probably worthwhile.  You have experienced one of the lows of research, when you get back to the high's you will appreciate them all the more for the contrast.

Congrats on solving the problem, thanks for the update :)

Perhaps I'm taking the OP too literally at his word, but my first inclination is to see it like this: an undergraduate tried his hand at research, had a predominantly negative experience, and now is not motivated to continue even though his advisor gave him something else to do.  Well, there is one obvious answer: don't continue with your research if you don't want to.  Whenever an undergraduate is doing mathematical research (TCS research counts), they are doing it for the purpose of getting a sense of whether they like it and want to continue with it more than any other purpose.  So if you feel strongly enough that you don't like it, it may well be that in fact you achieved what you were supposed to achieve in a fundamentally deeper sense than the one you are feeling bad about.  Most undergraduates doing mathematical research decide at some point that it is not really for them, at which point they stop.
To be honest, my experience with undergraduates doing mathematical research is that they are often rather fickle and flighty in their approach when viewed through the lens of a professional researcher.  I have spent hours, days or more trying to give undergraduates the training they need to work on a problem that I've chosen for them, only to hear from them next week that they are now interested in something entirely different, e.g. some pattern they saw in the numerical output of some code that they wrote.  Whether that is disappointing depends entirely on my expectations.  I now think that treating an undergraduate as a "non-positive year graduate student" is the wrong approach: in particular they should not be assigned a problem that one would expect an older student or researcher to spend several months working on.  Certainly they should not be given a problem such that a failure to solve it -- or even a complete neglect of it -- will have a significant negative impact on their advisor or anyone else.
Circling back to the situation: I worry that the OP has been placed in a situation which is "too serious" for an undergraduate student.  A little context is missing; e.g., the OP writes

I have been working as an undergraduate researcher in theoretical computer science for 7 months.

Does that just mean that you've been thinking about TCS for 7 months?  Are you getting paid to do it?  (Most undergraduates in the US are not paid for academic work they do during the academic year...but the OP may well not be in the US.)  Are you getting paid as a sort of undergraduate research assistant to your advisor?
There are some nuances in the situation that make it hard for me to read.  On the one hand, it's possible that your supervisor is doing a bang-up job: he gave you a problem that you were interested enough to work on for several months (already a successful undergraduate research experience, I claim).  You claimed to solve a piece of it, which is nice for you but not necessarily something that needed to be written up.  Then your advisor discovered that there actually was interest in what you had done, and was involved in the process of discovering a mistake in your writeup.  After that happened twice, he stepped in by sketching an approach of his own.  That sounds really supportive to me.  (I'm sorry that you put a lot of work into a writeup that he didn't comment on in detail, but: I've been on both sides of that situation.  It happens, too often, to good people.)  On the other hand, if your advisor actually expects you to function as someone who can mostly carry him through achieving his own research goals: when it comes to mathematical research, at least, that's very bad.  At the most you have a short internship as a mathematical researcher: it's his career, and the burden of responsibility needs to fall on him in every way.  If you are feeling bad because you think that you've derailed his own research plans or otherwise disappointed him: well, I think that's very poor behavior on his part.
To end, perhaps you should embrace the fickleness of undergraduate research.  Not feeling excited about the project?  Don't work on it...for now.  If there is something else that interests you, anything else, look at that instead, and talk to your supervisor about that if you choose.  It may well be that you could regain your positive feelings about TCS research by thinking about -- well, anything -- and when that occurs and/or some time has passed, you may actually enjoy returning to the problem and proposed solution your supervisor gave you.  (A big secret: I am a real life research mathematician, and giving up on something that isn't going well for a little while in order to regain enjoyment and confidence is something that I do very often.  Sometimes there is exactly one hard problem that I want to chip away at for days, weeks and months at a time...but more often, there isn't, and sometimes I wonder a bit at how hard people who only work on one thing are actually working.)  Or not, which (according to me!) is really okay.
Final word: don't do mathematical research if you don't enjoy it.  Seriously.
Added: I am concerned that my "final word" is not being understood as I meant it.  First of all, an equivalent version is "If you don't enjoy mathematical research, then don't do mathematical research."  Maybe this stops people from reading this as "don't do mathematical research [plus other words]"!  Second, the statement has to be construed in a reasonable way, and in fact anyone who is doing mathematical research has to construe it in a reasonable way for them.  Certainly I don't mean "If you wake up one (or two, or three...) days and have negative feelings about mathematical research -- or if you have one (or two, or three...) setbacks in your mathematical research -- then you're not cut out for it; just stop now"!  What I mean is "The main reason that people do mathematical research is because of the joy and sense of personal fulfillment it gives them -- not that it always makes them happy and fulfilled, but that in choosing which of the many things to do with their life, this choice seems to make them more happy and fulfilled than the alternatives."  There are extrinsic rewards to mathematical research as well -- if you are successful enough at it, you make more than enough money to survive, you have more control of your daily schedule than many other professionals, there are many opportunities for travel, and so forth -- but if you remove the intrinsic rewards, the extrinsic rewards don't stack up against other careers that a similarly talented, hard-working person could probably achieve.  Also not enjoying mathematics is not a failure and is not the same as being bad at it.  It almost seems silly to have to say this out loud, but: the people who do mathematical research as a career are not the ones who in all the world are the most talented or most successful at mathematics -- they are the ones who are talented and successful enough to get paid to do it and who value the activity enough to devote their lives to it.  Most undergraduates who do some mathematical research do not want to devote their lives to it.  That's not a character flaw or an intellectual weakness on their parts: there are just a lot of other valuable things to do.  Finally, I'm not saying "Look, most undergraduates quit, so you'll probably quit."  I'm saying "Most undergraduates quit, so the idea that you might quit should not be so horrific that you can't even contemplate it."  All things in moderation: if you have a bad experience with something, taking a small break from it, reassessing your commitment to it, adjusting your practice of it to rekindle your joy are all reasonable, healthy responses.  So is powering through the pain, sometimes.  These are all good things for us to have in our repertoire.

No, I'm not just "thinking about" TCS for 7 months. I'm not sure why it makes a difference but I've been getting paid for last 4 months as an undergraduate research assistant. And before that I was reading and working on papers that my advisor gave.

Whether you are getting paid for something definitely makes a difference, e.g. in what might happen if you stop doing the thing you are getting paid for.  Are you in the US?  (If not, even "undergraduate" can mean something very different!)  What are the duties of an undergraduate research assistant?  Can you just quit if you decide you don't like it?  (And a more difficult, but still pertinent question: do you know why your supervisor assigned you the task of fleshing out his argument rather than just doing it himself?)

Well, I never mentioned that I want to quit. Sometimes, I think about quiting but it's only because I feel like I won't be able to come up with something important, or beautiful. I enjoy mathematical research. However, I obviously do not enjoy making mistakes about things that I'm working for months. And it makes me feel bad about myself. I want to overcome it, as the title of the question suggests. However, your want me to quit it if I don't like it. To be honest, your suggestion has motivated me in a weird way. So thanks, anyway.

"However, your [sic] want me to quit if I don't like it."  Well, I certainly wanted to suggest the option.  Why are you doing something for which by far the largest inherent reward is the satisfaction you get from doing it if you don't get satisfaction from doing it?  I think you'll agree that's a fair question.  "I enjoy mathematical research." That's the first time you've said that!  As you say, it's very important, and the fact that my answer motivated you to say that is, in truth, not so "weird".

@errorist -- "To be honest, your suggestion has motivated me in a weird way" -- good for you.  Prof. Clark - giving the OP license to take a break is a positive contribution.  But the other stuff....  Most young people, and clearly this young person, already have more than enough self doubt.  It is not necessary for an external person to reinforce it.  -1.  (Also, a succinct non-constructive answer doesn't bother me as much as a loong one.)

@aparente001: I see nothing in my answer that reinforces self-doubt.  Is the idea that one might be happier doing Y rather than X really "self-doubt"?  That seems ridiculous to me.  We don't help students by denying that they have any options.  We help them by giving the options and conveying that it is okay for them to explore them.

@PeteL.Clark - I didn't see anyone denying there are options.  Look, I realize you had good intentions, and I realize you don't perceive your answer the way I do.  It is doubtful I will convince you that this type of answer can be hurtful, and it even more doubtful that talk of "denying they have any options", when no one did anything of the kind, will lead me to a more favorable opinion of your answer.  I rarely vote an answer down.  I felt you deserved an explanation.

"I didn't see anyone denying there are options."  The other answer writes "But you have to overcome these feelings." I'm not in any way upset or offended by your downvote, but I would certainly appreciate it if you would be attentive to facts and logic.  Also: almost anything can be hurtful when there is a lack of mutual understanding on the meaning of what has been said.  So I am willing to go out on a limb to be clear.  What part of my answer do you perceive as reinforcing self-doubt? It must be something...

It appears to be none of my business, but I guess the following might give some perspective. 1) As I understand your answer, you are suggesting the option of not doing mathematical research in the event that one does not actually enjoy it. This is an absolutely valid suggestion. 2) The question raises the "not enjoying" issue in a connection to an actual "failure" of some sort. Given 2) one may be inclined to read 1) as an advice to quit mathematical research if one has failed, and such a reading will understandably contribute to self-doubt.

@Peter: I certainly appreciate your comment.  Notice that I don't speak of "failure" at all but only "negative experiences".  As a research mathematician I know that not proving what you want to prove and/or finding mistakes in what you thought you proved are not signs that someone is not cut out to be a research mathematician: on the contrary, they are signs that one is doing mathematical research!  Since I don't address failure at all in my answer, I don't say this.  The accepted answer does provide reassurance in this direction, which is good.

But I want to be honest: yes, most research mathematicians have experiences like those described by the OP.  But how they respond to them is extremely subjective and individual.  I am a "successful" research mathematician, and when I find a mistake in work I've spent months on (or worse, published years ago), it still counts as a negative experience, to say the least!  If I made five times as many mistakes as I do or each mistake was five times as painful, I would have a terrible job.  So "Do you enjoy it, overall?" is not a euphemism for something else; it's the real, key question.

This is an excellent answer. Research is a job. Moreover, it is a hard job that very few people can do. Like any job it has its ups and downs but overall you have to enjoy it, otherwise you will not be happy doing a job you hate. This is something that newcomers to research should be told as soon as possible.

@PeteL.Clark - The accepted answer states "you have to overcome these feelings."*  Feelings can get you tied up in knots!  OP was overwhelmed by feelings of failure and [self-]anger, ... distracted by thinking about the mistake made.  The ideal would be for the OP to learn to distinguish between the soundness of an argument and his or her self-worth, regardless of how long this particular project and working relationship continues, and regardless of what field or type of project OP chooses to work on in future.

(cont.) With respect to your experiences and what you have learned over the years as a professor and advisor working with fickle and flighty undergraduates:  I invite you to share what you have to say about this in a separate question and answer.  In other words, modularize.  For future answers, you could include a link to that question where you think it might be relevant.

+100 for "The main reason that people do mathematical research is because of the joy and sense of personal fulfillment it gives them -- not that it always makes them happy and fulfilled, but that in choosing which of the many things to do with their life, this choice seems to make them more happy and fulfilled than the alternatives."

Okay. I was in a well respected PhD program for two years, doing research, when I got sick, and now I've been sick for 3 years unable to do math. I'm won't say what your experiencing isn't real or unpleasant, but I'd like to suggest I have some perspective to offer you. A lot of it comes from realizing unhealthy emotional habits doing math that contributed to the stress that brought me to where I am now, unable to do math.
Fundamentally, I believe the healthiest way to approach mathematical research is to truly and deeply appreciate your ability to exercise your mental faculties, your ability to ponder interesting ideas, and your abilities to think of interesting questions. This is something like, "Neat, summation by parts is a neat tool and it's neat how it can be used in all these sorts of problems and, wow, maybe it is useful in this problem in such-and-such a way," vs, "Gosh, my attempt to use summation by parts fails to solve the problem. I suck."
This is different from successfully solving problems. That is a fine goal, but if you allow it to dominate how you relate to doing math research, you will be stressed out all the time unless you happen to be wildly and luckily successful.
I'm suggesting an attitude of humility. With this sort of an attitude, you can more easily accept what everyone else tells you, that failing and making mistakes is a big part of research. Of course it will happen to you. It happens to others too, though you don't get the inside scoop into their research lives. Certainly some people appear to never fail, and maybe some people really are that successful, but envy will only stress you out and make you feel depressed.
You need to practice this by expressing wonder or thankfulness for what you do understand. Here are some examples.
"Wow. I actually do understand the problem statement!"
"Neat! People actually care about this problem, it impacts the world in some small way, and I get to participate in the community by thinking about it."
"It's neat that I was able to use [this clever integration by parts trick] in an attempted argument."
"I am thankful I have an opportunity to participate in the mathematical community and potentially write a paper."
"[Anything you think it positive: i.e., something about your experience, your paper, etc., you'd rather have than not have, no matter how small or trivial.]"
Fake it until you make it. If you think there is a modicum of merit in adopting the humble attitude, then you are being honest when you practice such thoughts.
The point is, if you approach things from a humbler perspective, the experience wasn't wasted even if you don't achieve your goal. And it really is a privilege to think about mathematics. If you find you cannot, not matter what you do, enjoy the process of thinking of mathematics and working through ideas on your own regardless of whether it is fruitful or not, then maybe it is true that research isn't your path.
I miss my days of research and have realized I love thinking about math on my own. Hope there's something useful here.

Focusing too much on your personal experience may have something to do with it - the world is bigger than your own self, connect to it.
Maybe find other motivations: e.g. "some economists out there just can't wait to use the methods you derive" or "theoretical CS is beautiful no matter how treacherous"
It also may be a case of burn-out. Usually those recedes with Rest-and-Recreation.
Or is it 're creation'? In the sense of trying to create something in an unrelated area, succeeding and regaining self-confidence by proving yourself you still have value (despite being just human and making mistakes).

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


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My (ex-)advisor is holding our paper hostage
I left a PhD program in statistics last August after nearly four years in the program. The department graciously allowed me to finish out my Masters, so I graduated in December and have since started a new job in a related but unusual field for my degree. One of my reasons for leaving the program was my relationship with my advisor, which was causing me daily stress that I decided was no longer worth enduring.
About a month before I decided to leave the program, I submitted what was to be the first paper of my dissertation to a well-regarded journal in our subfield. I was first author and my advisor was listed as second author. In December (right as I was about to graduate with a Masters), the paper returned as an acceptance with minor revisions. There were only a half dozen or so reviewer comments, mostly minor.
I got to work addressing the reviewers' concerns, which didn't take long. My advisor, however, raised a major concern. He insisted that one part of the algorithm described in our paper was incorrect and that I should fix it. I asked him why he thought it was wrong and his reply essentially boiled down to "I'm convinced it is wrong". I stubbornly refused to do the additional work of another proof until he could identify where the original error was. This led to a very contentious Zoom call where my advisor told me that we should re-check essentially every part of the algorithm - because if one part was wrong, then perhaps everything was.
I eventually did the proof he had asked for and showed that I had been right all along. I sent the proof to my advisor and asked him to read it so that we could submit the paper. He said he would, but now almost two months have gone by and I have not heard from him. My previous experience with him leads me to believe that this radio silence is intentional and that he has not just forgotten about the whole project.
My options are:
A) Do nothing and (presumably) let the paper go unpublished. Given my career trajectory, it is not hugely important to me that the paper be published, although it would be nice to see my name as first author.
B) Nudge my advisor for a response, potentially provoking a demand for more work that I consider superfluous. Dealing with my advisor any further will almost certainly cause me a great deal of stress (or relationship is very strained).
If you think I should take option B, how can I be clear that I do not wish to put much additional work into the project and believe it should be submitted now that I have answered every reviewer comment? Should I make an ultimatum, or try to offer some sort of compromise?

If the paper is accepted, why can't you just send a revised version to the publisher?

@Basia journals typically require the consent of all authors for the initial submission and any revisions. Submitting without informing or against the wishes of a coauthor is a big no-no.

@astronat isn't blocking the publishing just to spite your co-author even a bigger no-no?  If I were sure that the paper is worth it and the co-author is just being mean,  I'd write an ultimatum "I'm going to publish the paper as it is, if you don't want your name on it, tell me in the next X days"

@Basia I agree, that is probably the right strategy. From you comment I thought you were implying the OP should send the revised version back without telling their supervisor.

@astonat Sorry for not being clear enough. The informing part was obvious to me, I was just puzzled that the OP named two options: either giving up or working more on the already accepted paper

Your post leads me to believe that your advisor may not have contributed much to your paper and therefore might not even need to be a second author. Also if its already submitted, make the revisions and re-submit. Remember you are first author therefore you are the authority. If all else fails remove their contributions.

If you really don't care about the paper then A seems ok as long as the paper isn't published without you.
But you could nudge the professor and then decide what you want to do. If you get unreasonable demands then you can back away which should prevent the paper being published (ethically, at least). But it is possible that your worst fears won't be realized and you have a simple way forward.
But I would save any ultimatum for a later round after you hear a response to a request to submit. You want to be the "reasonable party" in any conversation.

Ask your supervisor what steps need to occur to get the paper published.  Request that a timeframe be established for each step.  Clearly state how much time you are able to contribute to the project (total and within the next month).
This is not a hostage situation.  This is an all-too-common disorganisation or negligence situation.  It can be hard to tell the difference, but in this case we can be sure it is not a hostage situation because you do not see any value in the hostage.


text:
Can IEEE, Elsevier, Springer detect multiple submissions to their journals?
If one wants to submit one's manuscript to multiple journals of a publisher (IEEE, Elsevier, Springer etc.), is it possible for a publisher to detect it? I mean if any publisher keeps a database of submitted manuscripts to crosscheck newly submitted manuscripts with the existing ones.

Plagiarism is excluded in the question because plag. means to crosscheck with already published work.

From one of the IEEE transactions: "IEEE takes the protection of intellectual property seriously. Accordingly, all submissions are filtered by CrossCheck, a powerful plagiarism detection software system. By submitting your work you agree to allow IEEE to screen your work. When plagiarism is detected, penalties can be severe and may include strict banning from publishing in all IEEE titles."

I'm wondering why this question was downvoted.

Related (actually, almost duplicate): How do conferences detect double submission?

I wonder why you ask. Are you intending to do this?

@Buffy Yes. I need my work to be reviewed by as many experts as possible within short span of time.

It is an extremely dangerous act. I recommend against it. Your reputation will probably suffer. If it is found out by anyone, it will likely be soon known by everyone.

@Daniel  If I had to guess, I would guess the down vote is due to the answer to Buffy's comment. Multi-submission is kind of aggravating. I would urge the OP not to do it, even if the chance of getting caught soon is small. Sooner or later you are likely to be in front of some kind of evaluation committee, for a job or a grant or something. And this sort of thing can suddenly jump up and bite you hard.

In the light of insightful comments and advices, I have changed my mind. Thanks to all.

@puppetsockreinstateMonica The downvote happened before my previous comment (and before Buffy's comment/question). I see nothing wrong with the OP's question hence my previous comment.

Surprisingly enough, they probably can't. Modern Editorial Management Systems can detect multiple submissions to the same journal, even if the previous submission was years ago, but the EMS still only works for that one journal. Inter-journal sharing does happen, but as far as I'm aware, it's not common and even then it's often only the reviewer pool. The editors of one journal cannot see which manuscripts are submitted to the other journal.
If you are detected by the publisher, the most likely reason is because one of the production staff handles both journals and noticed it. Alternatively, it's possible the editors of both journals invited the same reviewer who noticed it.

Depending on how narrow the relevant field is, there might also be a good chance that both editors pick the same reviewer, which will equally be noticed. All in all, it sounds like a good way to get blacklisted...

Good point, will add.


text:
What to do if I'm afraid that my idea will get stolen during review process?
I have an idea that I would like to publish. However, the idea is so simple that basically everyone in the field could reproduce the experiment that shows its benefit within a day or so.
What can I do to ensure that my idea is not stolen during the review process by a reviewer, for example?
If the reviewer holds back my paper and publishes it himself somewhere else, is there something I can do to prevent this?

Don't worry so much, work on multiple ideas.

Human brain is full ofideas. If one goes like that, something new will come. However, in peer-review process it is somewhat common. In that case, reviewers should follow peer-review ethics. If they are not following, then I would say they are not researchers.

Before you worry too much about this, ask yourself why an idea that is so "simple" isn't already published. Two common reasons are (1) everybody already knows it, even if nobody is quite sure who first discovered it, and (2) actually, it's not so good an idea as you think it is, and other people already know why it's no good.

@alephzero Or perhaps the idea isn't so simple, after all. It's often hard to judge how simple an idea really is, especially for the person who had that idea.

Assuming the journals you publish in allow it, you can submit your work to a preprint archive such as ArXiv.org. You can also put it up on a personal website.
Even if someone tries to scoop you, if you work is ever published, the date it was submitted for review should appear in the final article, giving your work precedence on any other. As for your concerns about reviewers stealing your work, there is not much else you can do besides the above. The peer review system is based on good faith, and hopefully you end up with ethical reviewers.

Editors can also be helpful if something like this happens as they know who the reviewers are.

First off, I would not worry too much about someone stealing your ideas.  A peer reviewed paper has already been seen by you, your advisor, the editor of the journal/conference and at least 1 other reviewer (probably more).  If a reviewer was to steal your idea, it would be trivially easy to prove he/she stole it - simply show the email from the thief where he/she reviewed it.
You should keep every submission, review (accepted and rejected), and editor note for papers you write.  Most researchers I know already do this (usually via email folders).